33 relations: Adjacency matrix, Algorithm, Alternating Turing machine, Aviezri Fraenkel, Big O notation, Chess, Complexity class, Computational complexity theory, Decision problem, Double exponential function, Draughts, DTIME, Exponential hierarchy, EXPSPACE, EXPTIME, Generalized game, Go (game), NEXPTIME, Non-deterministic Turing machine, NP (complexity), P (complexity), P versus NP problem, P-complete, Polynomial-time reduction, PSPACE, PSPACE-complete, Set (mathematics), Space hierarchy theorem, Sparse language, Time complexity, Time hierarchy theorem, Turing machine, 2-EXPTIME.

## Adjacency matrix

In mathematics, computer science and application areas such as sociology, an adjacency matrix is a means of representing which vertices (or nodes) of a graph are adjacent to which other vertices.

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## Algorithm

In mathematics and computer science, an algorithm is a self-contained step-by-step set of operations to be performed.

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## Alternating Turing machine

In computational complexity theory, an alternating Turing machine (ATM) is a non-deterministic Turing machine (NTM) with a rule for accepting computations that generalizes the rules used in the definition of the complexity classes NP and co-NP.

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## Aviezri Fraenkel

Aviezri Siegmund Fraenkel (אביעזרי פרנקל) (born June 7, 1929) is an Israeli mathematician who has made notable contributions to combinatorial game theory.

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## Big O notation

In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions.

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## Chess

Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an eight-by-eight grid.

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## Complexity class

In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.

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## Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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## Decision problem

In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters.

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## Double exponential function

A double exponential function is a constant raised to the power of an exponential function.

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## Draughts

Draughts or checkers (American English) is a group of strategy board games for two players which involve diagonal moves of uniform game pieces and mandatory captures by jumping over opponent pieces.

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## DTIME

In computational complexity theory, DTIME (or TIME) is the computational resource of computation time for a deterministic Turing machine.

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## Exponential hierarchy

In computational complexity theory, the exponential hierarchy is a hierarchy of complexity classes, which is an exponential time analogue of the polynomial hierarchy.

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## EXPSPACE

In complexity theory, EXPSPACE is the set of all decision problems solvable by a deterministic Turing machine in O(2p(n)) space, where p(n) is a polynomial function of n. (Some authors restrict p(n) to be a linear function, but most authors instead call the resulting class ESPACE.) If we use a nondeterministic machine instead, we get the class NEXPSPACE, which is equal to EXPSPACE by Savitch's theorem.

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## EXPTIME

In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems solvable by a deterministic Turing machine in O(2p(n)) time, where p(n) is a polynomial function of n. In terms of DTIME, We know and also, by the time hierarchy theorem and the space hierarchy theorem, that so at least one of the first three inclusions and at least one of the last three inclusions must be proper, but it is not known which ones are.

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## Generalized game

In computational complexity theory, a generalized game is a game that has been generalized so that it can be played on a board of any size.

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## Go (game)

* Go (囲碁,The full Japanese name igo is derived from its Chinese name weiqi, which roughly translates as "board game of surrounding"; see at Sensei's Library for more information. To differentiate the game Go from the common English verb to go, it is generally capitalized (Gao 2007) or, in events sponsored by the Ing Foundation, spelled goe. literal meaning: "encircling game", 바둑 The Korean word 'baduk' derives from the Middle Korean word 'Badok', the meaning of which is controversial; the more plausible etymologies include the suffix '-ok' added to 'Bad' creating the meaning 'flat and wide board', or the joining of 'Bad', meaning 'field', and 'Dok', meaning 'stone'. Less plausible etymologies include a derivation of 'Badukdok', referring to the playing pieces of the game, or a derivation from Chinese 排子, meaning 'to arrange pieces'.See) is a board game involving two players, that originated in ancient China more than 2,500 years ago.

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## NEXPTIME

In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic Turing machine using time 2n O(1) and unlimited space.

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## Non-deterministic Turing machine

In theoretical computer science, a Turing machine is a theoretical machine that is used in thought experiments to examine the abilities and limitations of computers.

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## NP (complexity)

In computational complexity theory, NP is one of the most fundamental complexity classes.

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## P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is one of the most fundamental complexity classes.

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## P versus NP problem

The P versus NP problem is a major unsolved problem in computer science.

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## P-complete

In complexity theory, the notion of P-complete decision problems is useful in the analysis of both.

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## Polynomial-time reduction

In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine.

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## PSPACE

In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space.

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## PSPACE-complete

In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time.

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## Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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## Space hierarchy theorem

In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more space, subject to certain conditions.

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## Sparse language

In computational complexity theory, a sparse language is a formal language (a set of strings) such that the complexity function, counting the number of strings of length n in the language, is bounded by a polynomial function of n. They are used primarily in the study of the relationship of the complexity class NP with other classes.

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## Time complexity

In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the length of the string representing the input.

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## Time hierarchy theorem

In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines.

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## Turing machine

A Turing machine is an abstract "machine" that manipulates symbols on a strip of tape according to a table of rules; to be more exact, it is a mathematical model that defines such a device.

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## 2-EXPTIME

In computational complexity theory, the complexity class 2-EXPTIME (sometimes called 2-EXP) is the set of all decision problems solvable by a deterministic Turing machine in O(22p(n)) time, where p(n) is a polynomial function of n. In terms of DTIME, We know 2-EXPTIME can also be reformulated as the space class AEXPSPACE, the problems that can be solved by an alternating Turing machine in exponential space.

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## Redirects here:

APSPACE, DEXPTIME, EXP, EXPTIME-complete, Exponential running time.