31 relations: Alternating Turing machine, Cambridge University Press, Closed timelike curve, Complement (complexity), Computational complexity theory, Context-sensitive language, Decision problem, Descriptive complexity theory, DSPACE, EXPSPACE, EXPTIME, Interactive proof system, IP (complexity), John Watrous (computer scientist), NL (complexity), Non-deterministic Turing machine, Nondeterministic algorithm, NP (complexity), P (complexity), PH (complexity), Polynomial, Polynomial-time reduction, PSPACE-complete, QIP (complexity), Quantum computing, Savitch's theorem, Second-order logic, Space hierarchy theorem, Transitive closure, True quantified Boolean formula, Turing machine.

## 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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## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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## Closed timelike curve

In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime that is "closed", returning to its starting point.

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## Complement (complexity)

In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers.

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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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## Context-sensitive language

In theoretical computer science, a context-sensitive language is a formal language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar).

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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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## Descriptive complexity theory

Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic needed to express the languages in them.

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## DSPACE

In computational complexity theory, DSPACE or SPACE is the computational resource describing the resource of memory space for a deterministic Turing machine.

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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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## Interactive proof system

In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties.

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## IP (complexity)

In computational complexity theory, the class IP (which stands for Interactive Polynomial time) is the class of problems solvable by an interactive proof system.

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## John Watrous (computer scientist)

John Harrison Watrous is a professor of computer science at the David R. Cheriton School of Computer Science at the University of Waterloo, a member of the Institute for Quantum Computing, an affiliate member of the Perimeter Institute for Theoretical Physics and a Fellow of the Canadian Institute for Advanced Research.

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## NL (complexity)

In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems which can be solved by a nondeterministic Turing machine using a logarithmic amount of memory 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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## Nondeterministic algorithm

In computer science, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm.

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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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## PH (complexity)

In computational complexity theory, the complexity class PH is the union of all complexity classes in the polynomial hierarchy: PH was first defined by Larry Stockmeyer.

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## Polynomial

In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

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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-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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## QIP (complexity)

In computational complexity theory, the class QIP, which stands for Quantum Interactive Polynomial time, is the quantum computing analogue of the classical complexity class IP, which is the set of problems solvable by an interactive proof system with a polynomial-time verifier and one computationally unbounded prover.

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## Quantum computing

Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.

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## Savitch's theorem

In computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministic and non-deterministic space complexity.

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## Second-order logic

In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.

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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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## Transitive closure

In mathematics, the transitive closure of a binary relation R on a set X is the transitive relation R+ on set X such that R+ contains R and R+ is minimal (Lidl and Pilz 1998:337).

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## True quantified Boolean formula

In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas.

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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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## Redirects here:

AP (complexity), APTIME, NPSPACE, P = PSPACE problem, PSPACE (complexity), PSPACE-Hard, PSPACE-hard, Polynomial space.