Answer: electron

Context: Tesla exhibited a pre-atomic understanding of physics in his writings; he disagreed with the theory of atoms being composed of smaller subatomic particles, stating there was no such thing as an electron creating an electric charge (he believed that if electrons existed at all, they were some fourth state of matter or "sub-atom" that could only exist in an experimental vacuum and that they had nothing to do with electricity).:249 Tesla believed that atoms are immutable—they could not change state or be split in any way. He was a believer in the 19th century concept of an all pervasive "ether" that transmitted electrical energy.

Question: What subatomic particle did Tesla deny the existence of?


Answer: ether

Question: What did he think was everywhere in the universe?


Answer: transmitted electrical energy

Question: What did he believe the ether did?


Answer: 19th

Question: To what century did the idea of ether belong?


Answer: Einstein's

Context: Tesla was generally antagonistic towards theories about the conversion of matter into energy.:247 He was also critical of Einstein's theory of relativity, saying:

Question: Whose theory did Tesla disagree with?


Answer: antagonistic

Question: What was Tesla's attitude toward the idea that matter could be turned into energy?


Answer: relativity

Question: Which theory of Einstein's did Tesla speak critically toward?


Answer: gravity

Context: Tesla claimed to have developed his own physical principle regarding matter and energy that he started working on in 1892, and in 1937, at age 81, claimed in a letter to have completed a "dynamic theory of gravity" that "[would] put an end to idle speculations and false conceptions, as that of curved space." He stated that the theory was "worked out in all details" and that he hoped to soon give it to the world. Further elucidation of his theory was never found in his writings.:309

Question: What "dynamic theory" did Tesla say he finished in 1937?


Answer: 1892

Question: When did Tesla start working on the problem of energy and matter?


Answer: curved

Question: What shape of space did Tesla consider a "false conception"?


Answer: 81

Question: How old was Tesla when he wrote that he'd completed his dynamic theory of gravity?


Answer: eugenics

Context: Tesla, like many of his era, became a proponent of an imposed selective breeding version of eugenics. His opinion stemmed from the belief that humans' "pity" had interfered with the natural "ruthless workings of nature," rather than from conceptions of a "master race" or inherent superiority of one person over another. His advocacy of it was, however, to push it further. In a 1937 interview, he stated:

Question: What idea was Tesla a fan of?


Answer: ruthless

Question: What was his belief as to what nature was supposed to be?


Answer: pity

Question: What attribute of humans interfered with nature's ruthlessness in Tesla's opinion?


Answer: 1937

Question: When did he talk about his beliefs in an interview?


Answer: women

Context: In 1926, Tesla commented on the ills of the social subservience of women and the struggle of women toward gender equality, and indicated that humanity's future would be run by "Queen Bees." He believed that women would become the dominant sex in the future.

Question: Who did Tesla think would run the world of the future?


Answer: 1926

Question: When did he talk about his thoughts on gender?


Answer: Queen Bees

Question: What term did he use for what he believed would be humanity's future rulers?


Answer: post-World War I

Context: Tesla made predictions about the relevant issues of a post-World War I environment in a printed article, "Science and Discovery are the great Forces which will lead to the Consummation of the War" (20 December 1914). Tesla believed that the League of Nations was not a remedy for the times and issues.[citation needed]

Question: The issues of what era did Tesla's article talk about?


Answer: Science and Discovery

Question: What were the "great Forces" mentioned in the article's title?


Answer: 20 December 1914

Question: When was the article published?


Answer: League of Nations

Question: What entity did Tesla believe would not be able to solve the problems of the time?


Answer: Orthodox Christian

Context: Tesla was raised an Orthodox Christian. Later in his life, he did not consider himself to be a "believer in the orthodox sense," and opposed religious fanaticism. Despite this, he had a profound respect for both Buddhism and Christianity.

Question: What religion did Tesla grow up in?


Answer: fanaticism

Question: What type of religious behavior was Tesla against?


Answer: Buddhism and Christianity

Question: Which two religions did Tesla express respect for?


Answer: "A Machine to End War"

Context: However, his religious views remain uncertain due to other statements that he made. For example, in his article, "A Machine to End War", published in 1937, Tesla stated:

Question: What article was published in 1937?


Answer: uncertain

Question: Because of certain statements what was the believed state of his religious views?


Answer: War

Question: In the article's title, what did the machine hope to end?


Answer: books and articles

Context: Tesla wrote a number of books and articles for magazines and journals. Among his books are My Inventions: The Autobiography of Nikola Tesla, compiled and edited by Ben Johnston; The Fantastic Inventions of Nikola Tesla, compiled and edited by David Hatcher Childress; and The Tesla Papers.

Question: What did Tesla write?


Answer: magazines and journals

Question: Who published Tesla's writings?


Answer: Ben Johnston

Question: Who edited Tesla's autobiography?


Answer: the web

Context: Many of Tesla's writings are freely available on the web, including the article "The Problem of Increasing Human Energy," published in The Century Magazine in 1900, and the article "Experiments With Alternate Currents Of High Potential And High Frequency," published in his book Inventions, Researches and Writings of Nikola Tesla.

Question: Where can a lot Tesla's writings be found?


Answer: 1900

Question: When was his article published in Century Magazine?


Answer: Inventions, Researches and Writings of Nikola Tesla.

Question: What was one of Tesla's books where articles can be read?


Answer: science fiction

Context: Tesla's legacy has endured in books, films, radio, TV, music, live theater, comics and video games. The impact of the technologies invented or envisioned by Tesla is a recurring theme in several types of science fiction.

Question: What kind of fiction is Tesla's work featured in?


Answer: books, films, radio, TV, music, live theater, comics and video games

Question: What kind of media can references to Tesla be found in


Answer: several

Question: How many types of science fiction have been impacted by Tesla?


Answer: Time magazine

Context: On Tesla's 75th birthday in 1931, Time magazine put him on its cover. The cover caption "All the world's his power house" noted his contribution to electrical power generation. He received congratulatory letters from more than 70 pioneers in science and engineering, including Albert Einstein.

Question: On which magazine's cover did Tesla appear in 1931


Answer: 75th birthday

Question: For what occasion was he put on the cover?


Answer: electrical power generation

Question: To which technology type that Tesla worked on did the caption refer to?


Answer: Einstein

Question: What famous person congratulated him?


Answer: more than 70

Question: How many other important people sent letters?


Answer: Computational complexity theory

Context: Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm.

Question: What branch of theoretical computer science deals with broadly classifying computational problems by difficulty and class of relationship?


Answer: inherent difficulty

Question: By what main attribute are computational problems classified utilizing computational complexity theory?


Answer: computational problems

Question: What is the term for a task that generally lends itself to being solved by a computer?


Answer: if its solution requires significant resources

Context: A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.

Question: What measure of a computational problem broadly defines the inherent difficulty of the solution?


Answer: mathematical models of computation

Question: What method is used to intuitively assess or quantify the amount of resources required to solve a computational problem?


Answer: time and storage

Question: What are two basic primary resources used to guage complexity?


Answer: number of gates in a circuit

Question: What unit is measured to determine circuit complexity?


Answer: determine the practical limits on what computers can and cannot do

Question: What practical role does defining the complexity of problems play in everyday computing?


Answer: analysis of algorithms and computability theory

Context: Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More precisely, it tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kind of problems can, in principle, be solved algorithmically.

Question: What two fields of theoretical computer science closely mirror computational complexity theory?


Answer: analysis of algorithms

Question: What field of computer science analyzes the resource requirements of a specific algorithm isolated unto itself within a given problem?


Answer: computational complexity theory

Question: What field of computer science analyzes all possible algorithms in aggregate to determine the resource requirements needed to solve to a given problem?


Answer: computability theory

Question: What field of computer science is primarily concerned with determining the likelihood of whether or not a problem can ultimately be solved using algorithms?


Answer: problem instance

Context: A computational problem can be viewed as an infinite collection of instances together with a solution for every instance. The input string for a computational problem is referred to as a problem instance, and should not be confused with the problem itself. In computational complexity theory, a problem refers to the abstract question to be solved. In contrast, an instance of this problem is a rather concrete utterance, which can serve as the input for a decision problem. For example, consider the problem of primality testing. The instance is a number (e.g. 15) and the solution is "yes" if the number is prime and "no" otherwise (in this case "no"). Stated another way, the instance is a particular input to the problem, and the solution is the output corresponding to the given input.

Question: What is the name given to the input string of a computational problem?


Answer: the problem

Question: In computational complexity theory, what is the term given to describe the baseline abstract question needing to be solved?


Answer: concrete

Question: Is a problem instance typically characterized as abstract or concrete?


Answer: instances

Question: What is another name for any given measure of input associated with a problem?


Answer: solution

Question: What is the general term used to describe the output to any given input in a problem instance?


Answer: 2000

Context: To further highlight the difference between a problem and an instance, consider the following instance of the decision version of the traveling salesman problem: Is there a route of at most 2000 kilometres passing through all of Germany's 15 largest cities? The quantitative answer to this particular problem instance is of little use for solving other instances of the problem, such as asking for a round trip through all sites in Milan whose total length is at most 10 km. For this reason, complexity theory addresses computational problems and not particular problem instances.

Question: By how many kilometers does the traveling salesman problem seek to classify a route between the 15 largest cities in Germany?


Answer: round trip through all sites in Milan

Question: What is one example of an instance that the quantitative answer to the traveling salesman problem fails to answer?


Answer: computational problems

Question: What does computational complexity theory most specifically seek to answer?


Answer: problem instance

Context: When considering computational problems, a problem instance is a string over an alphabet. Usually, the alphabet is taken to be the binary alphabet (i.e., the set {0,1}), and thus the strings are bitstrings. As in a real-world computer, mathematical objects other than bitstrings must be suitably encoded. For example, integers can be represented in binary notation, and graphs can be encoded directly via their adjacency matrices, or by encoding their adjacency lists in binary.

Question: In a computational problem, what can be described as a string over an alphabet?


Answer: binary alphabet

Question: What is the name of the alphabet is most commonly used in a problem instance?


Answer: bitstrings

Question: What is another term for the string of a problem instance?


Answer: binary notation

Question: In the encoding of mathematical objects, what is the way in which integers are commonly expressed?


Answer: adjacency matrices

Question: What is one way in which graphs can be encoded?


Answer: Decision problems

Context: Decision problems are one of the central objects of study in computational complexity theory. A decision problem is a special type of computational problem whose answer is either yes or no, or alternately either 1 or 0. A decision problem can be viewed as a formal language, where the members of the language are instances whose output is yes, and the non-members are those instances whose output is no. The objective is to decide, with the aid of an algorithm, whether a given input string is a member of the formal language under consideration. If the algorithm deciding this problem returns the answer yes, the algorithm is said to accept the input string, otherwise it is said to reject the input.

Question: What kind of problems are one of the main topics studied in computational complexity theory?


Answer: yes or no

Question: What are the two simple word responses to a decision problem?


Answer: 1 or 0

Question: What are the two integer responses to a decision problem?


Answer: yes

Question: What will the output be for a member of the language of a decision problem?


Answer: yes

Question: What answer denotes that an algorithm has accepted an input string?


Answer: arbitrary graph

Context: An example of a decision problem is the following. The input is an arbitrary graph. The problem consists in deciding whether the given graph is connected, or not. The formal language associated with this decision problem is then the set of all connected graphs—of course, to obtain a precise definition of this language, one has to decide how graphs are encoded as binary strings.

Question: What kind of graph is an example of an input used in a decision problem?


Answer: formal language

Question: What is the term for the set of all connected graphs related to this decision problem?


Answer: how graphs are encoded as binary strings

Question: What encoding decision needs to be made in order to determine an exact definition of the formal language?


Answer: a computational problem

Context: A function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem, that is, it isn't just yes or no. Notable examples include the traveling salesman problem and the integer factorization problem.

Question: A function problem is an example of what?


Answer: a single output

Question: How many outputs are expected for each input in a function problem?


Answer: A function problem

Question: The traveling salesman problem is an example of what type of problem?


Answer: the integer factorization problem

Question: In addition to the traveling salesman problem, what is another example of a function problem?


Answer: complex

Question: Is the output of a functional problem typically characterized by a simple or complex answer?


Answer: decision problems

Context: It is tempting to think that the notion of function problems is much richer than the notion of decision problems. However, this is not really the case, since function problems can be recast as decision problems. For example, the multiplication of two integers can be expressed as the set of triples (a, b, c) such that the relation a × b = c holds. Deciding whether a given triple is a member of this set corresponds to solving the problem of multiplying two numbers.

Question: How can function problems typically be restated?


Answer: set of triples

Question: If two integers are multiplied and output a value, what is this expression set called?


Answer: how much time the best algorithm requires to solve the problem

Context: To measure the difficulty of solving a computational problem, one may wish to see how much time the best algorithm requires to solve the problem. However, the running time may, in general, depend on the instance. In particular, larger instances will require more time to solve. Thus the time required to solve a problem (or the space required, or any measure of complexity) is calculated as a function of the size of the instance. This is usually taken to be the size of the input in bits. Complexity theory is interested in how algorithms scale with an increase in the input size. For instance, in the problem of finding whether a graph is connected, how much more time does it take to solve a problem for a graph with 2n vertices compared to the time taken for a graph with n vertices?

Question: What is a commonly used measurement used to determine the complexity of a computational problem?


Answer: the instance

Question: What is one variable on which the running time may be contingent?


Answer: as a function of the size of the instance

Question: How is the time needed to obtain the solution to a problem calculated?


Answer: bits

Question: In what unit is the size of the input measured?


Answer: an increase in the input size

Question: Complexity theory seeks to define the relationship between the scale of algorithms with respect to what other variable?


Answer: Cobham's thesis

Context: If the input size is n, the time taken can be expressed as a function of n. Since the time taken on different inputs of the same size can be different, the worst-case time complexity T(n) is defined to be the maximum time taken over all inputs of size n. If T(n) is a polynomial in n, then the algorithm is said to be a polynomial time algorithm. Cobham's thesis says that a problem can be solved with a feasible amount of resources if it admits a polynomial time algorithm.

Question: Whose thesis states that the solution to a problem is solvable with reasonable resources assuming it allows for a polynomial time algorithm?


Answer: the time taken

Question: If input size is is equal to n, what can respectively be assumed is the function of n?


Answer: worst-case time complexity

Question: What term corresponds to the maximum measurement of time across all functions of n?


Answer: T(n)

Question: How is worst-case time complexity written as an expression?


Answer: polynomial time algorithm

Question: Assuming that T represents a polynomial in T(n), what is the term given to the corresponding algorithm?


Answer: A Turing machine

Context: A Turing machine is a mathematical model of a general computing machine. It is a theoretical device that manipulates symbols contained on a strip of tape. Turing machines are not intended as a practical computing technology, but rather as a thought experiment representing a computing machine—anything from an advanced supercomputer to a mathematician with a pencil and paper. It is believed that if a problem can be solved by an algorithm, there exists a Turing machine that solves the problem. Indeed, this is the statement of the Church–Turing thesis. Furthermore, it is known that everything that can be computed on other models of computation known to us today, such as a RAM machine, Conway's Game of Life, cellular automata or any programming language can be computed on a Turing machine. Since Turing machines are easy to analyze mathematically, and are believed to be as powerful as any other model of computation, the Turing machine is the most commonly used model in complexity theory.

Question: What is the term for a mathematical model that theoretically represents a general computing machine?


Answer: an algorithm

Question: It is generally assumed that a Turing machine can solve anything capable of also being solved using what?


Answer: the Turing machine

Question: What is the most commonplace model utilized in complexity theory?


Answer: symbols

Question: What does a Turing machine handle on a strip of tape?


Answer: A deterministic Turing machine

Context: A deterministic Turing machine is the most basic Turing machine, which uses a fixed set of rules to determine its future actions. A probabilistic Turing machine is a deterministic Turing machine with an extra supply of random bits. The ability to make probabilistic decisions often helps algorithms solve problems more efficiently. Algorithms that use random bits are called randomized algorithms. A non-deterministic Turing machine is a deterministic Turing machine with an added feature of non-determinism, which allows a Turing machine to have multiple possible future actions from a given state. One way to view non-determinism is that the Turing machine branches into many possible computational paths at each step, and if it solves the problem in any of these branches, it is said to have solved the problem. Clearly, this model is not meant to be a physically realizable model, it is just a theoretically interesting abstract machine that gives rise to particularly interesting complexity classes. For examples, see non-deterministic algorithm.

Question: What is generally considered to be the most basic iteration of a Turing machine?


Answer: rules

Question: What fixed set of factors determine the actions of a deterministic Turing machine


Answer: A probabilistic Turing machine

Question: What is the term used to identify a deterministic Turing machine that has additional random bits?


Answer: A non-deterministic Turing machine

Question: What type of Turing machine is capable of multiple actions and extends into a variety of computational paths?


Answer: randomized algorithms

Question: What is the term given to algorithms that utilize random bits?


Answer: complexity classes

Context: Many types of Turing machines are used to define complexity classes, such as deterministic Turing machines, probabilistic Turing machines, non-deterministic Turing machines, quantum Turing machines, symmetric Turing machines and alternating Turing machines. They are all equally powerful in principle, but when resources (such as time or space) are bounded, some of these may be more powerful than others.

Question: Turing machines are commonly employed to define what?


Answer: time or space

Question: What are two factors that directly effect how powerful a Turing machine may or may not be?


Answer: probabilistic Turing machines, non-deterministic Turing machines

Question: In the determination of complexity classes, what are two examples of types of Turing machines?


Answer: random access machines

Context: Many machine models different from the standard multi-tape Turing machines have been proposed in the literature, for example random access machines. Perhaps surprisingly, each of these models can be converted to another without providing any extra computational power. The time and memory consumption of these alternate models may vary. What all these models have in common is that the machines operate deterministically.

Question: What is an example of a machine model that deviates from a generally accepted multi-tape Turing machine?


Answer: computational power

Question: In considering Turing machines and alternate variables, what measurement left unaffected by conversion between machine models?


Answer: time and memory

Question: What two resources commonly consumed by alternate models are typically known to vary?


Answer: the machines operate deterministically

Question: What commonality do alternate machine models, such as random access machines, share with Turing machines?


Answer: non-deterministic

Context: However, some computational problems are easier to analyze in terms of more unusual resources. For example, a non-deterministic Turing machine is a computational model that is allowed to branch out to check many different possibilities at once. The non-deterministic Turing machine has very little to do with how we physically want to compute algorithms, but its branching exactly captures many of the mathematical models we want to analyze, so that non-deterministic time is a very important resource in analyzing computational problems.

Question: What type of Turing machine can be characterized by checking multiple possibilities at the same time?


Answer: unusual resources

Question: What often affects or facilitates ease of analysis in computational problems?


Answer: mathematical models

Question: A non-deterministic Turing machine has the ability to capture what facet of useful analysis?


Answer: time

Question: What is the most critical resource in the analysis of computational problems associated with non-deterministic Turing machines?


Answer: state transitions

Context: For a precise definition of what it means to solve a problem using a given amount of time and space, a computational model such as the deterministic Turing machine is used. The time required by a deterministic Turing machine M on input x is the total number of state transitions, or steps, the machine makes before it halts and outputs the answer ("yes" or "no"). A Turing machine M is said to operate within time f(n), if the time required by M on each input of length n is at most f(n). A decision problem A can be solved in time f(n) if there exists a Turing machine operating in time f(n) that solves the problem. Since complexity theory is interested in classifying problems based on their difficulty, one defines sets of problems based on some criteria. For instance, the set of problems solvable within time f(n) on a deterministic Turing machine is then denoted by DTIME(f(n)).

Question: The time required to output an answer on a deterministic Turing machine is expressed as what?


Answer: difficulty

Question: Complexity theory classifies problems based on what primary attribute?


Answer: DTIME(f(n))

Question: What is the expression used to identify any given series of problems capable of being solved within time on a deterministic Turing machine?


Answer: time

Question: What is the most critical resource measured to in assessing the determination of a Turing machine's ability to solve any given set of problems?


Answer: complexity resources

Context: Analogous definitions can be made for space requirements. Although time and space are the most well-known complexity resources, any complexity measure can be viewed as a computational resource. Complexity measures are very generally defined by the Blum complexity axioms. Other complexity measures used in complexity theory include communication complexity, circuit complexity, and decision tree complexity.

Question: Time and space are both examples of what type of resource?


Answer: computational resource

Question: A complexity resource can also be described as what other type of resource?


Answer: Blum complexity axioms

Question: What is typically used to broadly define complexity measures?


Answer: Complexity measures

Question: Communication complexity is an example of what type of measure?


Answer: Complexity measures

Question: Decision tree is an example of what type of measure?


Answer: best, worst and average

Context: The best, worst and average case complexity refer to three different ways of measuring the time complexity (or any other complexity measure) of different inputs of the same size. Since some inputs of size n may be faster to solve than others, we define the following complexities:

Question: What are the three primary expressions used to represent case complexity?


Answer: complexity measure

Question: Case complexity likelihoods provide variable probabilities of what general measure?


Answer: time

Question: What is one common example of a critical complexity measure?


Answer: inputs

Question: Case complexities provide three likelihoods of what differing variable that remains the same size?


Answer: deterministic sorting algorithm quicksort

Context: For example, consider the deterministic sorting algorithm quicksort. This solves the problem of sorting a list of integers that is given as the input. The worst-case is when the input is sorted or sorted in reverse order, and the algorithm takes time O(n2) for this case. If we assume that all possible permutations of the input list are equally likely, the average time taken for sorting is O(n log n). The best case occurs when each pivoting divides the list in half, also needing O(n log n) time.

Question: What provides a solution to a list of integers provided as input that ned to be sorted?


Answer: worst-case

Question: When extensive time is required to sort integers, this represents what case complexity?


Answer: O(n2)

Question: What is the expression used to denote a worst case complexity as expressed by time taken?


Answer: the most efficient algorithm

Context: To classify the computation time (or similar resources, such as space consumption), one is interested in proving upper and lower bounds on the minimum amount of time required by the most efficient algorithm solving a given problem. The complexity of an algorithm is usually taken to be its worst-case complexity, unless specified otherwise. Analyzing a particular algorithm falls under the field of analysis of algorithms. To show an upper bound T(n) on the time complexity of a problem, one needs to show only that there is a particular algorithm with running time at most T(n). However, proving lower bounds is much more difficult, since lower bounds make a statement about all possible algorithms that solve a given problem. The phrase "all possible algorithms" includes not just the algorithms known today, but any algorithm that might be discovered in the future. To show a lower bound of T(n) for a problem requires showing that no algorithm can have time complexity lower than T(n).

Question: Classification of resources is contingent on determining the upper and lower bounds of minimum time required by what?


Answer: analysis of algorithms

Question: The analysis of a specific algorithm is typically assigned to what field of computational science?


Answer: lower bounds

Question: Which bound of time is more difficult to establish?


Answer: upper bound

Question: A specific algorithm demonstrating T(n) represents what measure of time complexity?


Answer: all possible algorithms

Question: What is the colloquial phrase used to convey the continuum of algorithms with unlimited availability irrespective of time?


Answer: big O notation

Context: Upper and lower bounds are usually stated using the big O notation, which hides constant factors and smaller terms. This makes the bounds independent of the specific details of the computational model used. For instance, if T(n) = 7n2 + 15n + 40, in big O notation one would write T(n) = O(n2).

Question: What expression is generally used to convey upper or lower bounds?


Answer: constant factors and smaller terms

Question: What does a big O notation hide?


Answer: T(n) = O(n2)

Question: How would one write T(n) = 7n2 + 15n + 40 in big O notation?


Answer: the computational model

Question: Big O notation provides autonomy to upper and lower bounds with relationship to what?


Answer: complexity classes

Context: Of course, some complexity classes have complicated definitions that do not fit into this framework. Thus, a typical complexity class has a definition like the following:

Question: What has complicated definitions that prevent classification into a framework?


Answer: framework

Question: Complexity classes are generally classified into what?


Answer: complicated definitions

Question: Difficulty in establishing a framework for complexity classes can be caused by what variable?


Answer: chosen machine model

Context: But bounding the computation time above by some concrete function f(n) often yields complexity classes that depend on the chosen machine model. For instance, the language {xx | x is any binary string} can be solved in linear time on a multi-tape Turing machine, but necessarily requires quadratic time in the model of single-tape Turing machines. If we allow polynomial variations in running time, Cobham-Edmonds thesis states that "the time complexities in any two reasonable and general models of computation are polynomially related" (Goldreich 2008, Chapter 1.2). This forms the basis for the complexity class P, which is the set of decision problems solvable by a deterministic Turing machine within polynomial time. The corresponding set of function problems is FP.

Question: Concrete bounding of computation time frequently produces complexity classes contingent upon what?


Answer: linear time

Question: A multi-tape Turing machine requires what type of time for a solution?


Answer: single-tape Turing machines

Question: A language solved in quadratic time implies the use of what type of Turing machine?


Answer: Cobham-Edmonds thesis

Question: What thesis specifies that a polynomial relationship exists within time complexities in a computational model?


Answer: complexity class P

Question: Decision problems capable of being solved by a deterministic Turing machine while maintaining adherence to polynomial time belong to what class?


Answer: time or space

Context: Many important complexity classes can be defined by bounding the time or space used by the algorithm. Some important complexity classes of decision problems defined in this manner are the following:

Question: What are two examples of measurements are bound within algorithms to establish complexity classes?


Answer: bounding

Question: What function is used by algorithms to define measurements like time or space?


Answer: complexity classes

Question: Bounding of time and space or similar measurements is often used by algorithms to define what?


Answer: BPP, ZPP and RP

Context: Other important complexity classes include BPP, ZPP and RP, which are defined using probabilistic Turing machines; AC and NC, which are defined using Boolean circuits; and BQP and QMA, which are defined using quantum Turing machines. #P is an important complexity class of counting problems (not decision problems). Classes like IP and AM are defined using Interactive proof systems. ALL is the class of all decision problems.

Question: What are three examples of complexity classes associated with definitions established by probabilistic Turing machines?


Answer: Boolean

Question: AC and NC are complexity classes typically associated with what type of circuit?


Answer: quantum

Question: BQP and QMA are examples of complexity classes most commonly associated with what type of Turing machine?


Answer: #P

Question: What is the expression used to represent a complexity class of counting problems?


Answer: Interactive

Question: IP and AM are most commonly defined by what type of proof system?


Answer: computation time

Context: For the complexity classes defined in this way, it is desirable to prove that relaxing the requirements on (say) computation time indeed defines a bigger set of problems. In particular, although DTIME(n) is contained in DTIME(n2), it would be interesting to know if the inclusion is strict. For time and space requirements, the answer to such questions is given by the time and space hierarchy theorems respectively. They are called hierarchy theorems because they induce a proper hierarchy on the classes defined by constraining the respective resources. Thus there are pairs of complexity classes such that one is properly included in the other. Having deduced such proper set inclusions, we can proceed to make quantitative statements about how much more additional time or space is needed in order to increase the number of problems that can be solved.

Question: What is an example of a measurement within a complexity class that would create a bigger set of problems if the bounds were relaxed?


Answer: DTIME(n2)

Question: In what expression can one expect to find DTIME(n)


Answer: time and space hierarchy theorems

Question: What theorems are responsible for determining questions of time and space requirements?


Answer: a proper hierarchy on the classes defined

Question: Resources are constrained by hierarchy theorems to produce what?


Answer: quantitative statements

Question: What kind of statement is made in the effort of establishing the time and space requirements needed to enhance the ultimate number of problems solved?


Answer: time and space hierarchy theorems

Context: The time and space hierarchy theorems form the basis for most separation results of complexity classes. For instance, the time hierarchy theorem tells us that P is strictly contained in EXPTIME, and the space hierarchy theorem tells us that L is strictly contained in PSPACE.

Question: What is the foundation for separation results within complexity classes?


Answer: EXPTIME

Question: What is responsible for constraining P according to the time hierarchy theorem?


Answer: PSPACE

Question: Within what variable is L constrained according to the space hierarchy theorem?


Answer: reduction

Context: Many complexity classes are defined using the concept of a reduction. A reduction is a transformation of one problem into another problem. It captures the informal notion of a problem being at least as difficult as another problem. For instance, if a problem X can be solved using an algorithm for Y, X is no more difficult than Y, and we say that X reduces to Y. There are many different types of reductions, based on the method of reduction, such as Cook reductions, Karp reductions and Levin reductions, and the bound on the complexity of reductions, such as polynomial-time reductions or log-space reductions.

Question: What concept is frequently used to define complexity classes?


Answer: another problem

Question: Reduction essentially takes one problem and converts into what?


Answer: reduces

Question: According to reduction, if X and Y can be solved by the same algorithm then X performs what function in relationship to Y?


Answer: Karp reductions and Levin reductions

Question: What are two examples of different types of reduction?


Answer: the bound on the complexity of reductions

Question: Polynomial time reductions are an example of what?


Answer: polynomial-time reduction

Context: The most commonly used reduction is a polynomial-time reduction. This means that the reduction process takes polynomial time. For example, the problem of squaring an integer can be reduced to the problem of multiplying two integers. This means an algorithm for multiplying two integers can be used to square an integer. Indeed, this can be done by giving the same input to both inputs of the multiplication algorithm. Thus we see that squaring is not more difficult than multiplication, since squaring can be reduced to multiplication.

Question: What is the most frequently employed type of reduction?


Answer: multiplying two integers

Question: What equates to a squared integer according to polynomial time reduction?


Answer: polynomial time

Question: What measurement of time is used in polynomial time reduction?


Answer: input

Question: What would need to remain constant in a multiplication algorithm to produce the same outcome whether multiplying or squaring two integers?


Answer: multiplication

Question: According to polynomial time reduction squaring can ultimately be logically reduced to what?


Answer: the type of reduction being used

Context: This motivates the concept of a problem being hard for a complexity class. A problem X is hard for a class of problems C if every problem in C can be reduced to X. Thus no problem in C is harder than X, since an algorithm for X allows us to solve any problem in C. Of course, the notion of hard problems depends on the type of reduction being used. For complexity classes larger than P, polynomial-time reductions are commonly used. In particular, the set of problems that are hard for NP is the set of NP-hard problems.

Question: The complexity of problems often depends on what?


Answer: if every problem in C can be reduced to X

Question: What would create a conflict between a problem X and problem C within the context of reduction?


Answer: solve any problem in C

Question: An algorithm for X which reduces to C would us to do what?


Answer: NP-hard

Question: A problem set that that is hard for the expression NP can also be stated how?


Answer: NP-complete

Context: If a problem X is in C and hard for C, then X is said to be complete for C. This means that X is the hardest problem in C. (Since many problems could be equally hard, one might say that X is one of the hardest problems in C.) Thus the class of NP-complete problems contains the most difficult problems in NP, in the sense that they are the ones most likely not to be in P. Because the problem P = NP is not solved, being able to reduce a known NP-complete problem, Π2, to another problem, Π1, would indicate that there is no known polynomial-time solution for Π1. This is because a polynomial-time solution to Π1 would yield a polynomial-time solution to Π2. Similarly, because all NP problems can be reduced to the set, finding an NP-complete problem that can be solved in polynomial time would mean that P = NP.

Question: The hardest problems in NP can be analogously written as what class of problems?


Answer: NP

Question: NP complete problems contain the lowest likelihood of being located in what problem class?


Answer: there is no known polynomial-time solution

Question: If P = NP is unsolved, and reduction is applied to a known NP-complete problem vis a vis Π2 to Π1, what conclusion can be drawn for Π1?


Answer: NP

Question: If polynomial time can be utilized within an NP-complete problem, what does the imply P is equal to?


Answer: P

Context: The complexity class P is often seen as a mathematical abstraction modeling those computational tasks that admit an efficient algorithm. This hypothesis is called the Cobham–Edmonds thesis. The complexity class NP, on the other hand, contains many problems that people would like to solve efficiently, but for which no efficient algorithm is known, such as the Boolean satisfiability problem, the Hamiltonian path problem and the vertex cover problem. Since deterministic Turing machines are special non-deterministic Turing machines, it is easily observed that each problem in P is also member of the class NP.

Question: What complexity class is characterized by a computational tasks and efficient algorithms?


Answer: Cobham–Edmonds thesis

Question: What hypothesis is associated with the complexity class of P viewed as a mathematical abstraction with efficient algorithmic functionality?


Answer: NP

Question: What complexity class is commonly characterized by unknown algorithms to enhance solvability?


Answer: Boolean satisfiability problem

Question: What is an example of a problem that rests within the NP complexity class?


Answer: Turing machines

Question: In what theoretical machine is it confirmed that a problem in P belies membership in the NP class?


Answer: more efficient solutions

Context: The question of whether P equals NP is one of the most important open questions in theoretical computer science because of the wide implications of a solution. If the answer is yes, many important problems can be shown to have more efficient solutions. These include various types of integer programming problems in operations research, many problems in logistics, protein structure prediction in biology, and the ability to find formal proofs of pure mathematics theorems. The P versus NP problem is one of the Millennium Prize Problems proposed by the Clay Mathematics Institute. There is a US$1,000,000 prize for resolving the problem.

Question: If P is ultimately proven to be equal tot NP, what effect would this have on the efficiency of problems?


Answer: protein structure prediction

Question: What is a particular problem in biology that would benefit from determining that P = NP?


Answer: $1,000,000

Question: What is the prize offered for finding a solution to P=NP?


Answer: Ladner

Context: It was shown by Ladner that if P ≠ NP then there exist problems in NP that are neither in P nor NP-complete. Such problems are called NP-intermediate problems. The graph isomorphism problem, the discrete logarithm problem and the integer factorization problem are examples of problems believed to be NP-intermediate. They are some of the very few NP problems not known to be in P or to be NP-complete.

Question: Who demonstrated that P= NP implies problems not present in P or NP-complete?


Answer: NP-intermediate problems

Question: What is the name for a problem that meets Ladner's assertion?


Answer: graph isomorphism problem

Question: What is an example of an NP-intermediate problem not known to exist in P or NP-complete?


Answer: The graph isomorphism problem

Context: The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate. The answer is not known, but it is believed that the problem is at least not NP-complete. If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level. Since it is widely believed that the polynomial hierarchy does not collapse to any finite level, it is believed that graph isomorphism is not NP-complete. The best algorithm for this problem, due to Laszlo Babai and Eugene Luks has run time 2O(√(n log(n))) for graphs with n vertices.

Question: What is the problem attributed to defining if two finite graphs are isomorphic?


Answer: NP-complete

Question: What class is most commonly not ascribed to the graph isomorphism problem in spite of definitive determination?


Answer: polynomial time hierarchy

Question: What finite hierarchy implies that the graph isomorphism problem is NP-complete?


Answer: second level

Question: To what level would the polynomial time hierarchy collapse if graph isomorphism is NP-complete?


Answer: Laszlo Babai and Eugene Luks

Question: Who are commonly associated with the algorithm typically considered the most effective with respect to finite polynomial hierarchy and graph isomorphism?


Answer: The integer factorization problem

Context: The integer factorization problem is the computational problem of determining the prime factorization of a given integer. Phrased as a decision problem, it is the problem of deciding whether the input has a factor less than k. No efficient integer factorization algorithm is known, and this fact forms the basis of several modern cryptographic systems, such as the RSA algorithm. The integer factorization problem is in NP and in co-NP (and even in UP and co-UP). If the problem is NP-complete, the polynomial time hierarchy will collapse to its first level (i.e., NP will equal co-NP). The best known algorithm for integer factorization is the general number field sieve, which takes time O(e(64/9)1/3(n.log 2)1/3(log (n.log 2))2/3) to factor an n-bit integer. However, the best known quantum algorithm for this problem, Shor's algorithm, does run in polynomial time. Unfortunately, this fact doesn't say much about where the problem lies with respect to non-quantum complexity classes.

Question: What computational problem is commonly associated with prime factorization?


Answer: k

Question: The integer factorization problem essentially seeks to determine if the value of of an input is less than what variable?


Answer: modern cryptographic systems

Question: That there currently exists no known integer factorization problem underpins what commonly used system?


Answer: the general number field sieve

Question: What is the most well-known algorithm associated with the integer factorization problem?


Answer: suspected to be unequal

Context: Many known complexity classes are suspected to be unequal, but this has not been proved. For instance P ⊆ NP ⊆ PP ⊆ PSPACE, but it is possible that P = PSPACE. If P is not equal to NP, then P is not equal to PSPACE either. Since there are many known complexity classes between P and PSPACE, such as RP, BPP, PP, BQP, MA, PH, etc., it is possible that all these complexity classes collapse to one class. Proving that any of these classes are unequal would be a major breakthrough in complexity theory.

Question: What is the unproven assumption generally ascribed to the value of complexity classes?


Answer: P ⊆ NP ⊆ PP ⊆ PSPACE

Question: What is an expression that can be used to illustrate the suspected inequality of complexity classes?


Answer: between P and PSPACE

Question: Where can the complexity classes RP, BPP, PP, BQP, MA, and PH be located?


Answer: Proving that any of these classes are unequal

Question: What evidence between and among complexity classes would signify a theoretical watershed for complexity theory?


Answer: co-NP

Context: Along the same lines, co-NP is the class containing the complement problems (i.e. problems with the yes/no answers reversed) of NP problems. It is believed that NP is not equal to co-NP; however, it has not yet been proven. It has been shown that if these two complexity classes are not equal then P is not equal to NP.

Question: In what complexity class do complement problems of NP problems exist?


Answer: reversed

Question: How do the yes/no answers of a complement problem of NP appear?


Answer: not equal

Question: What is commonly believed to be the value relationship between P and co-NP


Answer: P is not equal to NP

Question: What implication can be derived for P and NP if P and co-NP are established to be unequal?


Answer: L

Context: Similarly, it is not known if L (the set of all problems that can be solved in logarithmic space) is strictly contained in P or equal to P. Again, there are many complexity classes between the two, such as NL and NC, and it is not known if they are distinct or equal classes.

Question: What variable is associated with all problems solved within logarithmic space?


Answer: strictly contained in P or equal to P

Question: Though unkown, what are the most commonly ascribed attributes of L in relation to P


Answer: complexity classes

Question: What lies between L and P that prevents a definitive determination of the relationship between L and P?


Answer: NL and NC

Question: What are two complexity classes between L and P?


Answer: if they are distinct or equal classes

Question: What is unknown about the complexity classes between L and P that further prevents determining the value relationship between L and P?


Answer: intractable problems

Context: Problems that can be solved in theory (e.g., given large but finite time), but which in practice take too long for their solutions to be useful, are known as intractable problems. In complexity theory, problems that lack polynomial-time solutions are considered to be intractable for more than the smallest inputs. In fact, the Cobham–Edmonds thesis states that only those problems that can be solved in polynomial time can be feasibly computed on some computational device. Problems that are known to be intractable in this sense include those that are EXPTIME-hard. If NP is not the same as P, then the NP-complete problems are also intractable in this sense. To see why exponential-time algorithms might be unusable in practice, consider a program that makes 2n operations before halting. For small n, say 100, and assuming for the sake of example that the computer does 1012 operations each second, the program would run for about 4 × 1010 years, which is the same order of magnitude as the age of the universe. Even with a much faster computer, the program would only be useful for very small instances and in that sense the intractability of a problem is somewhat independent of technological progress. Nevertheless, a polynomial time algorithm is not always practical. If its running time is, say, n15, it is unreasonable to consider it efficient and it is still useless except on small instances.

Question: Problems capable of theoretical solutions but consuming unreasonable time in practical application are known as what?


Answer: exponential-time algorithms

Question: Intractable problems lacking polynomial time solutions necessarily negate the practical efficacy of what type of algorithm?


Answer: NP-complete problems

Question: If NP is not equal to P, viewed through this lens, what type of problems can also be considered intractable?


Answer: Presburger arithmetic

Context: What intractability means in practice is open to debate. Saying that a problem is not in P does not imply that all large cases of the problem are hard or even that most of them are. For example, the decision problem in Presburger arithmetic has been shown not to be in P, yet algorithms have been written that solve the problem in reasonable times in most cases. Similarly, algorithms can solve the NP-complete knapsack problem over a wide range of sizes in less than quadratic time and SAT solvers routinely handle large instances of the NP-complete Boolean satisfiability problem.

Question: What eponymous variation of arithmetic presents a decision problem not evidenced in P?


Answer: algorithms have been written

Question: Despite the Presburger problem, and in view of intractability, what has been done to establish solutions in reasonable periods of time?


Answer: NP-complete knapsack problem

Question: What is an example of a problem to which effective algorithms have provided a solution in spite of the intractability associated with the breadth of sizes?


Answer: in less than quadratic time

Question: How quickly can an algorithm solve an NP-complete knapsack problem?


Answer: NP-complete Boolean satisfiability problem

Question: What is the example of another problem characterized by large instances that is routinely solved by SAT handlers employing efficient algorithms?


Answer: foundations were laid out

Context: Before the actual research explicitly devoted to the complexity of algorithmic problems started off, numerous foundations were laid out by various researchers. Most influential among these was the definition of Turing machines by Alan Turing in 1936, which turned out to be a very robust and flexible simplification of a computer.

Question: What tactic did researchers employ to offset the former deficit of work surrounding the complexity of algorithmic problems?


Answer: Alan Turing

Question: Who was the most influential researcher among those grappling with the deficit of work surrounding the complexity posed by algorithmic problems?


Answer: Turing machines

Question: What theoretical device is attributed to Alan Turing?


Answer: 1936

Question: In what year was the Alan Turing's definitional model of a computing device received?


Answer: a computer

Question: In the most basic sense what did a Turing machine emulate?


Answer: On the Computational Complexity of Algorithms

Context: As Fortnow & Homer (2003) point out, the beginning of systematic studies in computational complexity is attributed to the seminal paper "On the Computational Complexity of Algorithms" by Juris Hartmanis and Richard Stearns (1965), which laid out the definitions of time and space complexity and proved the hierarchy theorems. Also, in 1965 Edmonds defined a "good" algorithm as one with running time bounded by a polynomial of the input size.

Question: What paper is commonly considered the bellwether ushering in systematic studies computational complexity?


Answer: Juris Hartmanis and Richard Stearns

Question: What individuals were responsible for authoring "On the Computational Complexity of Algorithms"?


Answer: 1965

Question: In what year was Hatmanis and Stearn's seminal work in computational complexity received?


Answer: time and space

Question: What complex measurements were defined by "On the Computational Complexity of Algorithms"?


Answer: 1965

Question: In what year did Edmond's characterize a "good" algorithm?


Answer: John Myhill

Context: Earlier papers studying problems solvable by Turing machines with specific bounded resources include John Myhill's definition of linear bounded automata (Myhill 1960), Raymond Smullyan's study of rudimentary sets (1961), as well as Hisao Yamada's paper on real-time computations (1962). Somewhat earlier, Boris Trakhtenbrot (1956), a pioneer in the field from the USSR, studied another specific complexity measure. As he remembers:

Question: Who provided a definition of linear bounded automata in 1960?


Answer: 1961

Question: In what year did Raymond Sullivan publish a study of rudimentary sets?


Answer: Hisao Yamada

Question: In 1962, who was responsible for the authorship of a paper published on real time-computations?


Answer: input encoding

Context: Even though some proofs of complexity-theoretic theorems regularly assume some concrete choice of input encoding, one tries to keep the discussion abstract enough to be independent of the choice of encoding. This can be achieved by ensuring that different representations can be transformed into each other efficiently.

Question: What is the concrete choice typically assumed by most complexity-theoretic theorems?


Answer: encoding

Question: In the effort of maintaining a level of abstraction, what choice is typically left independent?


Answer: Manuel Blum

Context: In 1967, Manuel Blum developed an axiomatic complexity theory based on his axioms and proved an important result, the so-called, speed-up theorem. The field really began to flourish in 1971 when the US researcher Stephen Cook and, working independently, Leonid Levin in the USSR, proved that there exist practically relevant problems that are NP-complete. In 1972, Richard Karp took this idea a leap forward with his landmark paper, "Reducibility Among Combinatorial Problems", in which he showed that 21 diverse combinatorial and graph theoretical problems, each infamous for its computational intractability, are NP-complete.

Question: Who is responsible for axiomatic complexity theory?


Answer: speed-up theorem

Question: What theorem was implicated by Manuel Blum's axioms?


Answer: "Reducibility Among Combinatorial Problems"

Question: What is the paper written by Richard Karp in 1972 that ushered in a new era of understanding between intractability and NP-complete problems?


Answer: 21

Question: How many combinatory and graph theoretical problems, formerly believed to be plagued by intractability, did Karp's paper address?


Answer: the curriculum.

Context: The role of teacher is often formal and ongoing, carried out at a school or other place of formal education. In many countries, a person who wishes to become a teacher must first obtain specified professional qualifications or credentials from a university or college. These professional qualifications may include the study of pedagogy, the science of teaching. Teachers, like other professionals, may have to continue their education after they qualify, a process known as continuing professional development. Teachers may use a lesson plan to facilitate student learning, providing a course of study which is called the curriculum.

Question: What is a course of study called?


Answer: pedagogy

Question: What is another name to describe the science of teaching?


Answer: university or college.

Question: Where do most teachers get their credentials from?


Answer: lesson plan

Question: What can a teacher use to help students learn?


Answer: school

Question: Where is a teacher most likely to be teaching at?


Answer: cultures

Context: A teacher's role may vary among cultures. Teachers may provide instruction in literacy and numeracy, craftsmanship or vocational training, the arts, religion, civics, community roles, or life skills.

Question: What factor may make a teacher's role vary?


Answer: numeracy

Question: What is similar to literacy that a teacher would teach?


Answer: craftsmanship

Question: What is similar to vocational training?


Answer: life skills

Question: What type of teaching would help the most with everyday life?


Answer: family member

Context: In some countries, formal education can take place through home schooling. Informal learning may be assisted by a teacher occupying a transient or ongoing role, such as a family member, or by anyone with knowledge or skills in the wider community setting.

Question: Who is most likely to teach a child at home?


Answer: home schooling

Question: If someone is being taught at their place of residence, what is it called?


Answer: formal

Question: What type of education is home schooling?


Answer: transient

Question: What is the opposite of an ongoing role of teaching?


Answer: knowledge or skills

Question: What would a community member need to teach informally?


Answer: spiritual

Context: Religious and spiritual teachers, such as gurus, mullahs, rabbis, pastors/youth pastors and lamas, may teach religious texts such as the Quran, Torah or Bible.

Question: What is another general name for a religious teacher?


Answer: religious

Question: What type of text is the Quran?


Answer: the Quran, Torah or Bible

Question: Name a text that might be used by a religious teacher to teach.


Answer: Religious and spiritual teachers

Question: Who would generally teach from a work like the Quran, Torah or Bible?


Answer: homeschooling

Context: Teaching may be carried out informally, within the family, which is called homeschooling, or in the wider community. Formal teaching may be carried out by paid professionals. Such professionals enjoy a status in some societies on a par with physicians, lawyers, engineers, and accountants (Chartered or CPA).

Question: What is another name for teaching within the family?


Answer: paid professionals.

Question: Who is most likely to be doing formal teaching?


Answer: Chartered

Question: What is another type of accountant other than a CPA?


Answer: the wider community

Question: In addition to teaching within the family, where else is informal teaching done?


Answer: paid professionals.

Question: Who is generally considered on the same level as physicians, lawyers, engineers, and accountants (Chartered or CPA)?


Answer: school functions

Context: A teacher's professional duties may extend beyond formal teaching. Outside of the classroom teachers may accompany students on field trips, supervise study halls, help with the organization of school functions, and serve as supervisors for extracurricular activities. In some education systems, teachers may have responsibility for student discipline.

Question: What could a teacher help in organizing?


Answer: extracurricular

Question: What would type of activities would require a teacher to take on a supervisor role?


Answer: study halls

Question: What would type of studying would require a teacher to take on a supervisor role?


Answer: teachers

Question: Who might be responsible for student discipline?


Answer: teacher's colleges

Context: There are a variety of bodies designed to instill, preserve and update the knowledge and professional standing of teachers. Around the world many governments operate teacher's colleges, which are generally established to serve and protect the public interest through certifying, governing and enforcing the standards of practice for the teaching profession.

Question: What do government's run that affects teachers?


Answer: to serve and protect the public interest

Question: Why would a teacher's college exist?


Answer: the public

Question: Who would a teacher's college be protecting?


Answer: teachers

Question: Who is taught at teacher's colleges?


Answer: standards of practice

Question: Teacher's colleges certify, govern and enforce what for teachers?


Answer: members

Context: The functions of the teacher's colleges may include setting out clear standards of practice, providing for the ongoing education of teachers, investigating complaints involving members, conducting hearings into allegations of professional misconduct and taking appropriate disciplinary action and accrediting teacher education programs. In many situations teachers in publicly funded schools must be members in good standing with the college, and private schools may also require their teachers to be college peoples. In other areas these roles may belong to the State Board of Education, the Superintendent of Public Instruction, the State Education Agency or other governmental bodies. In still other areas Teaching Unions may be responsible for some or all of these duties.

Question: Who could be the subjects of a teacher's college investigation?


Answer: allegations of professional misconduct

Question: What could someone be investigated for?


Answer: teacher's colleges

Question: A teacher must be a member in good standing with what entity in many situations?


Answer: teacher's colleges

Question: Who might take disciplinary action against a teacher?


Answer: teacher's colleges

Question: Who might be charged with accrediting teacher education programs?


Answer: outdoors

Context: In education, teachers facilitate student learning, often in a school or academy or perhaps in another environment such as outdoors. A teacher who teaches on an individual basis may be described as a tutor.

Question: Where might a teacher teach that is not inside a building?


Answer: tutor

Question: What is the name for a teacher of just one person?


Answer: academy

Question: Where is another indoor location for a teacher other than a school?


Answer: facilitate student learning

Question: What is the role of teachers in education?


Answer: informal

Context: The objective is typically accomplished through either an informal or formal approach to learning, including a course of study and lesson plan that teaches skills, knowledge and/or thinking skills. Different ways to teach are often referred to as pedagogy. When deciding what teaching method to use teachers consider students' background knowledge, environment, and their learning goals as well as standardized curricula as determined by the relevant authority. Many times, teachers assist in learning outside of the classroom by accompanying students on field trips. The increasing use of technology, specifically the rise of the internet over the past decade, has begun to shape the way teachers approach their roles in the classroom.

Question: What is another way of learning that is not formal?


Answer: pedagogy

Question: What is a name for the different ways to instruct students?


Answer: field trips

Question: What is a typical name for learning that is not inside of the classroom?


Answer: increasing use of technology

Question: What has started to change the way teachers teach in the classroom, generally?


Answer: the internet

Question: What has risen to be a factor in teaching today?


Answer: skill

Context: The objective is typically a course of study, lesson plan, or a practical skill. A teacher may follow standardized curricula as determined by the relevant authority. The teacher may interact with students of different ages, from infants to adults, students with different abilities and students with learning disabilities.

Question: What objective would be labeled as practical?


Answer: the relevant authority

Question: Who would decide on the curricula that is consistent and standard?


Answer: learning

Question: What type of disability would a teacher help a student with?


Answer: infants

Question: What is the youngest student a teacher might have?


Answer: standardized

Question: What type of curricula is it that a teacher may likely follow?


Answer: particular skills

Context: Teaching using pedagogy also involve assessing the educational levels of the students on particular skills. Understanding the pedagogy of the students in a classroom involves using differentiated instruction as well as supervision to meet the needs of all students in the classroom. Pedagogy can be thought of in two manners. First, teaching itself can be taught in many different ways, hence, using a pedagogy of teaching styles. Second, the pedagogy of the learners comes into play when a teacher assesses the pedagogic diversity of his/her students and differentiates for the individual students accordingly. For example, an experienced teacher and parent described the place of a teacher in learning as follows: "The real bulk of learning takes place in self-study and problem solving with a lot of feedback around that loop. The function of the teacher is to pressure the lazy, inspire the bored, deflate the cocky, encourage the timid, detect and correct individual flaws, and broaden the viewpoint of all. This function looks like that of a coach using the whole gamut of psychology to get each new class of rookies off the bench and into the game."

Question: What would a teacher assess the levels of a student on?


Answer: self-study and problem solving

Question: In what areas does most of the learning take place?


Answer: encourage

Question: What would a teacher do for someone who is timid?


Answer: deflate

Question: What would a teacher do for someone who is cocky?


Answer: a coach

Question: What function is a teacher's role similar to?


Answer: the relationship between teachers and children

Context: Perhaps the most significant difference between primary school and secondary school teaching is the relationship between teachers and children. In primary schools each class has a teacher who stays with them for most of the week and will teach them the whole curriculum. In secondary schools they will be taught by different subject specialists each session during the week and may have ten or more different teachers. The relationship between children and their teachers tends to be closer in the primary school where they act as form tutor, specialist teacher and surrogate parent during the course of the day.

Question: What's the biggest difference in the teaching relationship for primary and secondary school?


Answer: the whole curriculum

Question: What does a teacher teach in primary school?


Answer: different subject specialists

Question: Who teaches in secondary schools?


Answer: primary school

Question: Which type of school has a closer teacher-child relationship?


Answer: surrogate

Question: What type of parenting role does a teacher take on?


Answer: alternative

Context: This is true throughout most of the United States as well. However, alternative approaches for primary education do exist. One of these, sometimes referred to as a "platoon" system, involves placing a group of students together in one class that moves from one specialist to another for every subject. The advantage here is that students learn from teachers who specialize in one subject and who tend to be more knowledgeable in that one area than a teacher who teaches many subjects. Students still derive a strong sense of security by staying with the same group of peers for all classes.

Question: What type of approaches for primary school are available that are different than the norm?


Answer: platoon

Question: What type of system takes students from one specialist to another for each subject?


Answer: staying with the same group of peers for all classes

Question: In a platoon style teaching, what gives the children security?


Answer: knowledgeable

Question: The teacher's in a platoon style teaching are usually more _____?


Answer: United States

Question: What country is this teaching subject discussing?


Answer: Co-teaching

Context: Co-teaching has also become a new trend amongst educational institutions. Co-teaching is defined as two or more teachers working harmoniously to fulfill the needs of every student in the classroom. Co-teaching focuses the student on learning by providing a social networking support that allows them to reach their full cognitive potential. Co-teachers work in sync with one another to create a climate of learning.

Question: What is a new trend in teaching?


Answer: two or more

Question: How many teachers are usually involved when co-teaching?


Answer: learning

Question: What does co-teaching get the students to focus on?


Answer: harmoniously

Question: How do co-teachers work with each other to fulfill the needs of students?


Answer: social networking support

Question: What type of support does co-teaching provide?


Answer: corporal punishment

Context: Throughout the history of education the most common form of school discipline was corporal punishment. While a child was in school, a teacher was expected to act as a substitute parent, with all the normal forms of parental discipline open to them.

Question: What was the usual type of school discipline?


Answer: substitute parent

Question: What was the teacher's role while the child was with them?


Answer: all the normal forms of parental discipline

Question: What types of discipline did the teacher have access to?


Answer: the most common

Question: How common of a type was corporal punishment in schools?


Answer: While a child was in school

Question: When could a teacher act in the role of a parent?


Answer: one of the most common

Context: In past times, corporal punishment (spanking or paddling or caning or strapping or birching the student in order to cause physical pain) was one of the most common forms of school discipline throughout much of the world. Most Western countries, and some others, have now banned it, but it remains lawful in the United States following a US Supreme Court decision in 1977 which held that paddling did not violate the US Constitution.

Question: How common was the form of corporal punishment in the past?


Answer: Most Western countries

Question: Where is corporal punishment no longer practiced?


Answer: United States

Question: What Western country is corporal punishment still allowed?


Answer: Supreme Court

Question: What U.S. entity said that corporal punishment was Constitutional?


Answer: physical pain

Question: What does corporal punishment cause a student?


Answer: 30

Context: 30 US states have banned corporal punishment, the others (mostly in the South) have not. It is still used to a significant (though declining) degree in some public schools in Alabama, Arkansas, Georgia, Louisiana, Mississippi, Oklahoma, Tennessee and Texas. Private schools in these and most other states may also use it. Corporal punishment in American schools is administered to the seat of the student's trousers or skirt with a specially made wooden paddle. This often used to take place in the classroom or hallway, but nowadays the punishment is usually given privately in the principal's office.

Question: How many US states do no practice corporal punishment?


Answer: the South

Question: Where is corporal punishment practiced the most?


Answer: declining

Question: Is corporal punishment increasing or declining in the South?


Answer: a specially made wooden paddle

Question: What tool is used in corporal punishment?


Answer: privately in the principal's office

Question: Where is corporal punishment usually performed these days?


Answer: caning

Context: Official corporal punishment, often by caning, remains commonplace in schools in some Asian, African and Caribbean countries. For details of individual countries see School corporal punishment.

Question: What is a common practice in official corporal punishment?


Answer: some Asian, African and Caribbean countries

Question: What countries is corporal punishment still a normal practice?


Answer: see School corporal punishment.

Question: Where can you find more information on a country's practices?


Answer: detention

Context: Currently detention is one of the most common punishments in schools in the United States, the UK, Ireland, Singapore and other countries. It requires the pupil to remain in school at a given time in the school day (such as lunch, recess or after school); or even to attend school on a non-school day, e.g. "Saturday detention" held at some schools. During detention, students normally have to sit in a classroom and do work, write lines or a punishment essay, or sit quietly.

Question: What is a common punishment in Singapore?


Answer: detention

Question: What is a common punishment in the UK and Ireland?


Answer: in schools

Question: Where does the pupil remain while in detention


Answer: quietly

Question: If a detention requires a pupil to just sit there, how are they required to sit?


Answer: lines or a punishment essay

Question: If a detention asks the student to write, what do they write?


Answer: assertive

Context: A modern example of school discipline in North America and Western Europe relies upon the idea of an assertive teacher who is prepared to impose their will upon a class. Positive reinforcement is balanced with immediate and fair punishment for misbehavior and firm, clear boundaries define what is appropriate and inappropriate behavior. Teachers are expected to respect their students; sarcasm and attempts to humiliate pupils are seen as falling outside of what constitutes reasonable discipline.[verification needed]

Question: What type of teacher is required in the Western Europe model of discipline?


Answer: immediate and fair punishment for misbehavior

Question: What is the balance for positive reinforcement?


Answer: firm, clear boundaries

Question: What type of boundaries help to define the way kids behave?


Answer: sarcasm and attempts to humiliate pupils

Question: What is not considered appropriate disclipine?


Answer: respect

Question: What are teachers expected to give their students?


Answer: some teachers and parents

Context: Whilst this is the consensus viewpoint amongst the majority of academics, some teachers and parents advocate a more assertive and confrontational style of discipline.[citation needed] Such individuals claim that many problems with modern schooling stem from the weakness in school discipline and if teachers exercised firm control over the classroom they would be able to teach more efficiently. This viewpoint is supported by the educational attainment of countries—in East Asia for instance—that combine strict discipline with high standards of education.[citation needed]

Question: Who wants a more confrontational type of discipline?


Answer: East Asia

Question: What countries are used as an example of harsher discipline with successful education?


Answer: weakness in school discipline

Question: What do critics think the cause of problems with modern schooling is?


Answer: a more assertive and confrontational style

Question: What type of discipline do critics want to see?


Answer: Japan

Context: It's not clear, however that this stereotypical view reflects the reality of East Asian classrooms or that the educational goals in these countries are commensurable with those in Western countries. In Japan, for example, although average attainment on standardized tests may exceed those in Western countries, classroom discipline and behavior is highly problematic. Although, officially, schools have extremely rigid codes of behavior, in practice many teachers find the students unmanageable and do not enforce discipline at all.

Question: What country has higher scores on standardized tests than the U.S.?


Answer: Japan

Question: What country has such unmanageable students that many teachers do not discipline them?


Answer: Japan

Question: What country has a problem with classroom discipline, even though scores on tests are high?


Answer: Japan

Question: What country's schools have codes of behavior that are very strict?


Answer: 40 to 50 students

Context: Where school class sizes are typically 40 to 50 students, maintaining order in the classroom can divert the teacher from instruction, leaving little opportunity for concentration and focus on what is being taught. In response, teachers may concentrate their attention on motivated students, ignoring attention-seeking and disruptive students. The result of this is that motivated students, facing demanding university entrance examinations, receive disproportionate resources. Given the emphasis on attainment of university places, administrators and governors may regard this policy as appropriate.

Question: What class sizes can make keeping order difficult?


Answer: instruction

Question: If the teacher focuses on maintaining order, what does this take time away from?


Answer: motivated students

Question: Who may teachers focus on, in order to prioritize attention?


Answer: attention-seeking and disruptive students

Question: Who may teachers ignore, in order to prioritize attention?


Answer: motivated students

Question: Who ends up getting more of the teacher's resources in this scenario?


Answer: popularly based authority

Context: Sudbury model democratic schools claim that popularly based authority can maintain order more effectively than dictatorial authority for governments and schools alike. They also claim that in these schools the preservation of public order is easier and more efficient than anywhere else. Primarily because rules and regulations are made by the community as a whole, thence the school atmosphere is one of persuasion and negotiation, rather than confrontation since there is no one to confront. Sudbury model democratic schools' proponents argue that a school that has good, clear laws, fairly and democratically passed by the entire school community, and a good judicial system for enforcing these laws, is a school in which community discipline prevails, and in which an increasingly sophisticated concept of law and order develops, against other schools today, where rules are arbitrary, authority is absolute, punishment is capricious, and due process of law is unknown.

Question: What type of authority do Sudbury schools prefer?


Answer: governments

Question: In addition to schools, where else is popularly based authority effective?


Answer: persuasion and negotiation

Question: What is the atmosphere in a school using popularly based authority?


Answer: easier and more efficient

Question: In schools using popularly based authority, what is public order like?


Answer: good, clear laws

Question: What must be passed using democratic means by the entire school community?


Answer: enthusiasm

Context: Since teachers can affect how students perceive the course materials, it has been found that teachers who showed enthusiasm towards the course materials and students can affect a positive learning experience towards the course materials. On teacher/course evaluations, it was found that teachers who have a positive disposition towards the course content tend to transfer their passion to receptive students. These teachers do not teach by rote but attempt to find new invigoration for the course materials on a daily basis. One of the difficulties in this approach is that teachers may have repeatedly covered a curriculum until they begin to feel bored with the subject which in turn bores the students as well. Students who had enthusiastic teachers tend to rate them higher than teachers who didn't show much enthusiasm for the course materials.

Question: What must a teacher show towards the course materials for increase learning?


Answer: passion

Question: What gets transferred to students who are receptive to the teacher?


Answer: teach by rote

Question: What do these teachers NOT do?


Answer: higher

Question: How do students rate teachers that they feel are enthusiastic?


Answer: teacher enthusiasm

Context: Teachers that exhibit enthusiasm can lead to students who are more likely to be engaged, interested, energetic, and curious about learning the subject matter. Recent research has found a correlation between teacher enthusiasm and students' intrinsic motivation to learn and vitality in the classroom. Controlled, experimental studies exploring intrinsic motivation of college students has shown that nonverbal expressions of enthusiasm, such as demonstrative gesturing, dramatic movements which are varied, and emotional facial expressions, result in college students reporting higher levels of intrinsic motivation to learn. Students who experienced a very enthusiastic teacher were more likely to read lecture material outside of the classroom.

Question: What increases student's motivation to learn?


Answer: read lecture material

Question: Students exposed to an enthusiastic teacher usually did what more often outside class?


Answer: nonverbal expressions of enthusiasm

Question: What is dramatic gesturing an example of?


Answer: Controlled, experimental studies

Question: What type of studies explored student motivation?


Answer: higher

Question: Nonverbal expressions resulted in what kind of levels of motivation to learn?


Answer: self-determined

Context: There are various mechanisms by which teacher enthusiasm may facilitate higher levels of intrinsic motivation. Teacher enthusiasm may contribute to a classroom atmosphere full of energy and enthusiasm which feed student interest and excitement in learning the subject matter. Enthusiastic teachers may also lead to students becoming more self-determined in their own learning process. The concept of mere exposure indicates that the teacher's enthusiasm may contribute to the student's expectations about intrinsic motivation in the context of learning. Also, enthusiasm may act as a "motivational embellishment"; increasing a student's interest by the variety, novelty, and surprise of the enthusiastic teacher's presentation of the material. Finally, the concept of emotional contagion, may also apply. Students may become more intrinsically motivated by catching onto the enthusiasm and energy of the teacher.[citation needed]

Question: Enthusiastic teachers may cause students to become more ____ about their learning process?


Answer: enthusiasm

Question: What may cause "motivational embellishment"?


Answer: emotional contagion

Question: What is the term for catching the motivation expressed by the teacher?


Answer: Teacher enthusiasm

Question: What might cause a higher student interest in learning the presented subject?


Answer: student-teacher relationships

Context: Research shows that student motivation and attitudes towards school are closely linked to student-teacher relationships. Enthusiastic teachers are particularly good at creating beneficial relations with their students. Their ability to create effective learning environments that foster student achievement depends on the kind of relationship they build with their students. Useful teacher-to-student interactions are crucial in linking academic success with personal achievement. Here, personal success is a student's internal goal of improving himself, whereas academic success includes the goals he receives from his superior. A teacher must guide his student in aligning his personal goals with his academic goals. Students who receive this positive influence show stronger self-confidence and greater personal and academic success than those without these teacher interactions.

Question: What is student motivation about school linked to?


Answer: beneficial

Question: What type of relationships do enthusiastic teachers cause?


Answer: the goals he receives from his superior.

Question: What does a student's academic goals include?


Answer: aligning his personal goals with his academic goals.

Question: What should a teacher guide a student in?


Answer: student motivation and attitudes towards school

Question: What is strongly linked to good student-teacher relationships?


Answer: friendly and supportive

Context: Students are likely to build stronger relations with teachers who are friendly and supportive and will show more interest in courses taught by these teachers. Teachers that spend more time interacting and working directly with students are perceived as supportive and effective teachers. Effective teachers have been shown to invite student participation and decision making, allow humor into their classroom, and demonstrate a willingness to play.

Question: Students show more interest in classes taught by what type of teachers?


Answer: friendly and supportive

Question: Students build stronger relationships with what type of teachers?


Answer: interacting and working directly with students

Question: What do supportive teachers spend more time doing?


Answer: effective

Question: Humor is a part of the classroom for what type of teacher?


Answer: enthusiasm about the students

Context: The way a teacher promotes the course they are teaching, the more the student will get out of the subject matter. The three most important aspects of teacher enthusiasm are enthusiasm about teaching, enthusiasm about the students, and enthusiasm about the subject matter. A teacher must enjoy teaching. If they do not enjoy what they are doing, the students will be able to tell. They also must enjoy being around their students. A teacher who cares for their students is going to help that individual succeed in their life in the future. The teacher also needs to be enthusiastic about the subject matter they are teaching. For example, a teacher talking about chemistry needs to enjoy the art of chemistry and show that to their students. A spark in the teacher may create a spark of excitement in the student as well. An enthusiastic teacher has the ability to be very influential in the young students life.

Question: What is the second aspect of teacher enthusiasm?


Answer: enthusiastic

Question: What does a teacher need to be with regards to their subject matter?


Answer: in the student

Question: A teacher's spark may create a spark where?


Answer: very influential

Question: What can an enthusiastic teacher be to a young student?


Answer: teaching

Question: What is important for a teacher to enjoy?


Answer: sexual misconduct

Context: Misconduct by teachers, especially sexual misconduct, has been getting increased scrutiny from the media and the courts. A study by the American Association of University Women reported that 9.6% of students in the United States claim to have received unwanted sexual attention from an adult associated with education; be they a volunteer, bus driver, teacher, administrator or other adult; sometime during their educational career.

Question: What is the largest type of misconduct being reviewed by the media?


Answer: 9.6%

Question: How many students have received unwanted sexual attention from a teacher or other education figure?


Answer: United States

Question: What country is this statistic for?


Answer: sometime during their educational career.

Question: What is the time period of this statistic?


Answer: American Association of University Women

Question: Who conducted this survey?


Answer: England

Context: A study in England showed a 0.3% prevalence of sexual abuse by any professional, a group that included priests, religious leaders, and case workers as well as teachers. It is important to note, however, that the British study referenced above is the only one of its kind and consisted of "a random ... probability sample of 2,869 young people between the ages of 18 and 24 in a computer-assisted study" and that the questions referred to "sexual abuse with a professional," not necessarily a teacher. It is therefore logical to conclude that information on the percentage of abuses by teachers in the United Kingdom is not explicitly available and therefore not necessarily reliable. The AAUW study, however, posed questions about fourteen types of sexual harassment and various degrees of frequency and included only abuses by teachers. "The sample was drawn from a list of 80,000 schools to create a stratified two-stage sample design of 2,065 8th to 11th grade students"Its reliability was gauged at 95% with a 4% margin of error.

Question: Where was it shown to have a 0.3% prevalence of sexual abuse by professionals?


Answer: priests, religious leaders, and case workers as well as teachers

Question: What was the definition of professionals, for this study?


Answer: 2,869

Question: How many people were involved in the study?


Answer: The AAUW study

Question: What study covered subjects in 80,000 schools?


Answer: United States

Context: In the United States especially, several high-profile cases such as Debra LaFave, Pamela Rogers, and Mary Kay Letourneau have caused increased scrutiny on teacher misconduct.

Question: Where has there been very well-known cases of teacher misconduct?


Answer: increased scrutiny on teacher misconduct

Question: What has been the result of this publicity?


Answer: Fears of being labelled a pedophile or hebephile

Context: Chris Keates, the general secretary of National Association of Schoolmasters Union of Women Teachers, said that teachers who have sex with pupils over the age of consent should not be placed on the sex offenders register and that prosecution for statutory rape "is a real anomaly in the law that we are concerned about." This has led to outrage from child protection and parental rights groups. Fears of being labelled a pedophile or hebephile has led to several men who enjoy teaching avoiding the profession. This has in some jurisdictions reportedly led to a shortage of male teachers.

Question: Why have some men avoided becoming teachers?


Answer: Chris Keates

Question: Who is the general secretary for the National Association of Schoolmasters Union of Women Teachers?


Answer: child protection and parental rights groups

Question: A statement made by Chris Keates caused issues with whom?


Answer: a shortage of male teachers

Question: What has the avoidance of men to become teachers caused, in some areas?


Answer: the sex offenders register

Question: What register did Chris Keates think that some teachers should not be placed on?


Answer: occupational stress

Context: Teachers face several occupational hazards in their line of work, including occupational stress, which can negatively impact teachers' mental and physical health, productivity, and students' performance. Stress can be caused by organizational change, relationships with students, fellow teachers, and administrative personnel, working environment, expectations to substitute, long hours with a heavy workload, and inspections. Teachers are also at high risk for occupational burnout.

Question: What can hurt a teacher's mental and physical health?


Answer: long hours

Question: What, when combined with a large workload, can contribute to occupational stress?


Answer: occupational burnout

Question: What is something that teacher's are at a high risk for?


Answer: stress

Question: What can be the result of a change in an organization?


Answer: occupational stress

Question: What, on the part of a teacher, can result in a decrease in student performance


Answer: 42%

Context: A 2000 study found that 42% of UK teachers experienced occupational stress, twice the figure for the average profession. A 2012 study found that teachers experienced double the rate of anxiety, depression, and stress than average workers.

Question: How many teachers were found to have felt occupational stress in a 2000 study?


Answer: UK

Question: Where was the 2000 study conducted?


Answer: twice the figure for the average profession

Question: How much higher was the 42% occupation stress figure, compared to other jobs?


Answer: 2012

Question: Which study showed double the rate of anxiety?


Answer: average workers

Question: The 2012 study showed teachers experienced more stress than whom?


Answer: several

Context: There are several ways to mitigate the occupational hazards of teaching. Organizational interventions, like changing teachers' schedules, providing support networks and mentoring, changing the work environment, and offering promotions and bonuses, may be effective in helping to reduce occupational stress among teachers. Individual-level interventions, including stress-management training and counseling, are also used to relieve occupational stress among teachers.

Question: How many ways are available to help reduce the stress of teaching?


Answer: Organizational interventions

Question: What is providing support networks considered to be?


Answer: Individual-level interventions

Question: What is stress-management training considered to be?


Answer: occupational stress among teachers

Question: What might offering bonuses help reduce?


Answer: Organizational interventions

Question: What type of intervention would changing the work environment be?