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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 that have exponential runtime, i.e., that are 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. 

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph.

## Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

## 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.

## Aviezri Fraenkel

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

## Big O notation

Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.

## Chess

Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid.

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## Complexity class

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

## Computability theory

Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.

## Computational complexity theory

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.

## Decision problem

In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.

## Double exponential function

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

## Draughts

Draughts (British English) 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.

## 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.

## EXPTIME

In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that have exponential runtime, i.e., that are 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.

## Generalized game

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

## Go (game)

Go is an abstract strategy board game for two players, in which the aim is to surround more territory than the opponent.

## Halting problem

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.

## 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).

## 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.

## P versus NP problem

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

## P-complete

In complexity theory, a decision problem is P-complete (complete for the complexity class '''P''') if it is in P and every problem in P can be reduced to it by an appropriate reduction.

## 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.

## 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.

## Set (mathematics)

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

## 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.

## 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.

## Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

## Time hierarchy theorem

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

## Turing machine

A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.

## 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.

## References

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