10 relations: Big O notation, Complexity class, Computational complexity theory, Decision problem, DTIME, EXPTIME, Polynomial-time reduction, SIAM Journal on Computing, Symposium on Foundations of Computer Science, Turing machine.

## 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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## 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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## DTIME

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

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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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## 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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## SIAM Journal on Computing

The SIAM Journal on Computing (SICOMP) is a scientific journal focusing on the mathematical and formal aspects of computer science.

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## Symposium on Foundations of Computer Science

FOCS, the Annual IEEE Symposium on Foundations of Computer Science, is an academic conference in the field of theoretical computer science.

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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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