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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. [1]

## Algorithm

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

## Arthur–Merlin protocol

In computational complexity theory, an Arthur&ndash;Merlin protocol is an interactive proof system in which the verifier's coin tosses are constrained to be public (i.e. known to the prover too).

## Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

## Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

## Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

Christmas traditions vary from country to country.

## Complete (complexity)

In computational complexity theory, a computational problem is complete for a complexity class if it is, in a technical sense, among the "hardest" (or "most expressive") problems in the complexity class.

## Complexity class

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

## 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.

## Crossing number (graph theory)

In graph theory, the crossing number of a graph is the lowest number of edge crossings of a plane drawing of the graph.

## 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.

## Existential theory of the reals

In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form where F(X_1,\dots X_n) is a quantifier-free formula involving equalities and inequalities of real polynomials.

## 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.

## Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

## Graph isomorphism problem

The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.

## International Symposium on Graph Drawing

The International Symposium on Graph Drawing (GD) is an annual academic conference in which researchers present peer reviewed papers on graph drawing, information visualization of network information, geometric graph theory, and related topics.

## Karp's 21 NP-complete problems

In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.

## L (complexity)

In computational complexity theory, L (also known as LSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space.

## Log-space reduction

In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space.

## Many-one reduction

In computability theory and computational complexity theory, a many-one reduction is a reduction which converts instances of one decision problem into instances of a second decision problem.

## NC (complexity)

In complexity theory, the class NC (for "Nick's Class") is the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of processors.

## 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.

## NP (complexity)

In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.

## NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

## NP-hardness

NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".

## New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

## New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

## New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

## P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.

## 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 hierarchy

In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes P, NP and co-NP to oracle machines.

## 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.

## 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.

## Reduction (complexity)

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem.

## Richard M. Karp

Richard Manning Karp (born January 3, 1935) is an American computer scientist and computational theorist at the University of California, Berkeley.

## Stephen Cook

Stephen Arthur Cook, (born December 14, 1939) is an American-Canadian computer scientist and mathematician who has made major contributions to the fields of complexity theory and proof complexity.

## Subroutine

In computer programming, a subroutine is a sequence of program instructions that performs a specific task, packaged as a unit.

## Time complexity

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

## Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).

## Truth-table reduction

In computability theory, a truth-table reduction is a reduction from one set of natural numbers to another.

## Turing reduction

In computability theory, a Turing reduction from a problem A to a problem B, is a reduction which solves A, assuming the solution to B is already known (Rogers 1967, Soare 1987).

## 2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

## 2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

## References

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