NP-completeness and P versus NP problem

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Difference between NP-completeness and P versus NP problem

NP-completeness vs. P versus NP problem

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes. The P versus NP problem is a major unsolved problem in computer science.

ACM SIGACT

ACM SIGACT or SIGACT is the Association for Computing Machinery Special Interest Group on Algorithms and Computation Theory, whose purpose is support of research in theoretical computer science.

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Advanced Encryption Standard

The Advanced Encryption Standard (AES), also known by its original name Rijndael, is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.

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Algorithm

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

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Boolean satisfiability problem

In computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.

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Clay Mathematics Institute

The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.

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Co-NP

In computational complexity theory, co-NP is a complexity class.

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Co-NP-complete

In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in co-NP can be reformulated as a special case of any co-NP-complete problem with only polynomial overhead.

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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.

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Cook–Levin theorem

In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete.

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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.

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Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

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Gerhard J. Woeginger

Gerhard J. Woeginger is an Austrian mathematician and computer scientist who works in Germany as a professor at RWTH Aachen University, where he chairs the algorithms and complexity group in the department of computer science.

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Graph isomorphism

In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H such that any two vertices u and v of G are adjacent in G if and only if ƒ(u) and ƒ(v) are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism being a structure-preserving bijection.

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Graph isomorphism problem

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

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Introduction to Algorithms

Introduction to Algorithms is a book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.

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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.

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Knapsack problem

The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

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Lance Fortnow

Lance Jeremy Fortnow (born August 15, 1963) is a computer scientist known for major results in computational complexity and interactive proof systems.

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List of NP-complete problems

This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems.

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List of unsolved problems in computer science

This article is a list of unsolved problems in computer science.

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List of unsolved problems in mathematics

Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, and yet many mathematical problems, both major and minor, still remain unsolved.

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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 (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.

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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".

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P (complexity)

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

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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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Presburger arithmetic

Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929.

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Randomized algorithm

A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic.

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Reduction (complexity)

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

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Scott Aaronson

Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and David J. Bruton Jr.

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SIAM Journal on Computing

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

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Subset sum problem

In computer science, the subset sum problem is an important problem in complexity theory and cryptography.

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Theoretical computer science

Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.

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Time complexity

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

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Travelling salesman problem

The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.

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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.

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