Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!
 

P versus NP problem

+ Save concept

The P versus NP problem is a major unsolved problem in computer science. [1]

146 relations: ACM SIGACT, Advanced Encryption Standard, AKS primality test, Alexander Razborov, Algorithm, Anil Nerode, Annals of Mathematics, Artificial intelligence, Association for Computing Machinery, Average-case complexity, Avi Wigderson, Aviezri Fraenkel, Big O notation, Bonnie Berger, Boolean satisfiability problem, Certificate (complexity), Chess, Clay Mathematics Institute, Co-NP, Co-NP-complete, Cobham's thesis, Complexity class, Composite number, Computational complexity theory, Computer programming, Computer science, Constructive proof, Cook–Levin theorem, Cornell University, Cryptographic hash function, David Eppstein, Decision problem, Descriptive complexity theory, Deterministic automaton, Discrete logarithm, Donald Knuth, Economics, Entscheidungsproblem, Eugene M. Luks, EXPTIME, F. Thomson Leighton, Fermat's Last Theorem, First-order logic, Fixed-point combinator, Game complexity, Game theory, General number field sieve, Gerhard J. Woeginger, Graph (discrete mathematics), Graph isomorphism, ..., Graph isomorphism problem, Halting problem, HP Labs, Independence (mathematical logic), Information-theoretic security, Integer factorization, Integer programming, Introduction to Algorithms, IP (complexity), John Forbes Nash Jr., John Markoff, John von Neumann, Journal of Combinatorial Theory, Journal of the Operational Research Society, Karp's 21 NP-complete problems, Knapsack problem, Kurt Gödel, Lance Fortnow, Latin square, László Babai, Leonid Levin, Linear programming, List of NP-complete problems, List of unsolved problems in computer science, List of unsolved problems in mathematics, Martin Grötschel, Massachusetts Institute of Technology, Michael O. Rabin, Millennium Prize Problems, MIT Press, Moshe Vardi, Multipartite graph, National Security Agency, Natural proof, Neil Immerman, Non-deterministic Turing machine, NP (complexity), NP-completeness, NP-hardness, One-way function, Operations research, Oracle machine, P (complexity), Peano axioms, Pearson Education, PH (complexity), Philosophy, Polymath Project, Polynomial, Polynomial hierarchy, Polynomial-time reduction, Presburger arithmetic, Princeton University, Protein structure prediction, PSPACE, Public-key cryptography, Quantum algorithm, Quantum computing, Randomized algorithm, Reduction (complexity), Rice University, Richard Lipton, Robert M. Solovay, RSA (cryptosystem), Russell Impagliazzo, Scott Aaronson, Second-order logic, Sharp-P-complete, Shor's algorithm, SIAM Journal on Computing, Signature (logic), Simplex algorithm, Stephen Cook, Steven Rudich, String (computer science), Subset sum problem, Sudoku, Symmetric-key algorithm, Symposium on Theoretical Aspects of Computer Science, The New Yorker, The Simpsons, Theoretical computer science, Theory of computation, Time complexity, Time hierarchy theorem, Total order, Travelling Salesman (2012 film), Travelling salesman problem, Treehouse of Horror VI, Triple DES, Turing machine, Undecidable problem, Unique games conjecture, Universal quantification, W. H. Freeman and Company, Zermelo–Fraenkel set theory. Expand index (96 more) »

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.

New!!: P versus NP problem and ACM SIGACT · See more »

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.

New!!: P versus NP problem and Advanced Encryption Standard · See more »

AKS primality test

The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, computer scientists at the Indian Institute of Technology Kanpur, on August 6, 2002, in a paper titled "PRIMES is in P".

New!!: P versus NP problem and AKS primality test · See more »

Alexander Razborov

Aleksandr Aleksandrovich Razborov (Алекса́ндр Алекса́ндрович Разбо́ров; born February 16, 1963), sometimes known as Sasha Razborov, is a Soviet and Russian mathematician and computational theorist.

New!!: P versus NP problem and Alexander Razborov · See more »

Algorithm

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

New!!: P versus NP problem and Algorithm · See more »

Anil Nerode

Anil Nerode (born 1932) is an American mathematician.

New!!: P versus NP problem and Anil Nerode · See more »

Annals of Mathematics

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.

New!!: P versus NP problem and Annals of Mathematics · See more »

Artificial intelligence

Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals.

New!!: P versus NP problem and Artificial intelligence · See more »

Association for Computing Machinery

The Association for Computing Machinery (ACM) is an international learned society for computing.

New!!: P versus NP problem and Association for Computing Machinery · See more »

Average-case complexity

In computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the algorithm, averaged over all possible inputs.

New!!: P versus NP problem and Average-case complexity · See more »

Avi Wigderson

Avi Wigderson (אבי ויגדרזון; born 9 September 1956) is an Israeli mathematician and computer scientist.

New!!: P versus NP problem and Avi Wigderson · See more »

Aviezri Fraenkel

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

New!!: P versus NP problem and Aviezri Fraenkel · See more »

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.

New!!: P versus NP problem and Big O notation · See more »

Bonnie Berger

Bonnie Anne Berger is an American mathematician and computer scientist, who works as the Simons professor of mathematics and professor of electrical engineering and computer science at the Massachusetts Institute of Technology.

New!!: P versus NP problem and Bonnie Berger · See more »

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.

New!!: P versus NP problem and Boolean satisfiability problem · See more »

Certificate (complexity)

In computational complexity theory, a certificate (also called a witness) is a string that certifies the answer to a computation, or certifies the membership of some string in a language.

New!!: P versus NP problem and Certificate (complexity) · See more »

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.

New!!: P versus NP problem and Chess · See more »

Christmas

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

New!!: P versus NP problem and Christmas · See more »

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.

New!!: P versus NP problem and Christmas and holiday season · See more »

Christmas Eve

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

New!!: P versus NP problem and Christmas Eve · See more »

Christmas traditions

Christmas traditions vary from country to country.

New!!: P versus NP problem and Christmas traditions · See more »

Clay Mathematics Institute

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

New!!: P versus NP problem and Clay Mathematics Institute · See more »

Co-NP

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

New!!: P versus NP problem and Co-NP · See more »

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.

New!!: P versus NP problem and Co-NP-complete · See more »

Cobham's thesis

Cobham's thesis, also known as Cobham–Edmonds thesis (named after Alan Cobham and Jack Edmonds), asserts that computational problems can be feasibly computed on some computational device only if they can be computed in polynomial time; that is, if they lie in the complexity class P (PTIME).

New!!: P versus NP problem and Cobham's thesis · See more »

Complexity class

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

New!!: P versus NP problem and Complexity class · See more »

Composite number

A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.

New!!: P versus NP problem and Composite number · See more »

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.

New!!: P versus NP problem and Computational complexity theory · See more »

Computer programming

Computer programming is the process of building and designing an executable computer program for accomplishing a specific computing task.

New!!: P versus NP problem and Computer programming · See more »

Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

New!!: P versus NP problem and Computer science · See more »

Constructive proof

In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object.

New!!: P versus NP problem and Constructive proof · See more »

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.

New!!: P versus NP problem and Cook–Levin theorem · See more »

Cornell University

Cornell University is a private and statutory Ivy League research university located in Ithaca, New York.

New!!: P versus NP problem and Cornell University · See more »

Cryptographic hash function

A cryptographic hash function is a special class of hash function that has certain properties which make it suitable for use in cryptography.

New!!: P versus NP problem and Cryptographic hash function · See more »

David Eppstein

David Arthur Eppstein (born 1963) is an American computer scientist and mathematician.

New!!: P versus NP problem and David Eppstein · See more »

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.

New!!: P versus NP problem and Decision problem · See more »

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.

New!!: P versus NP problem and Descriptive complexity theory · See more »

Deterministic automaton

In computer science, a deterministic automaton is a concept of automata theory in which the outcome of a transition from one state to another is determined by the input.

New!!: P versus NP problem and Deterministic automaton · See more »

Discrete logarithm

In the mathematics of the real numbers, the logarithm logb a is a number x such that, for given numbers a and b. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that.

New!!: P versus NP problem and Discrete logarithm · See more »

Donald Knuth

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

New!!: P versus NP problem and Donald Knuth · See more »

Economics

Economics is the social science that studies the production, distribution, and consumption of goods and services.

New!!: P versus NP problem and Economics · See more »

Entscheidungsproblem

In mathematics and computer science, the Entscheidungsproblem (German for "decision problem") is a challenge posed by David Hilbert in 1928.

New!!: P versus NP problem and Entscheidungsproblem · See more »

Eugene M. Luks

Eugene Michael Luks (born circa 1940) is an American mathematician and computer scientist, a professor emeritus of computer and information science at the University of Oregon.

New!!: P versus NP problem and Eugene M. Luks · See more »

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.

New!!: P versus NP problem and EXPTIME · See more »

F. Thomson Leighton

Frank Thomson "Tom" Leighton (born 1956) is the CEO of Akamai Technologies, the company he co-founded with Daniel Lewin in 1998.

New!!: P versus NP problem and F. Thomson Leighton · See more »

Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.

New!!: P versus NP problem and Fermat's Last Theorem · See more »

First-order logic

First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

New!!: P versus NP problem and First-order logic · See more »

Fixed-point combinator

In computer science's combinatory logic, a fixed-point combinator (or fixpoint combinator) is a higher-order function fix that, for any function f that has an attractive fixed point, returns a fixed point x of that function.

New!!: P versus NP problem and Fixed-point combinator · See more »

Game complexity

Combinatorial game theory has several ways of measuring game complexity.

New!!: P versus NP problem and Game complexity · See more »

Game theory

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".

New!!: P versus NP problem and Game theory · See more »

General number field sieve

In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than.

New!!: P versus NP problem and General number field sieve · See more »

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.

New!!: P versus NP problem and Gerhard J. Woeginger · See more »

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".

New!!: P versus NP problem and Graph (discrete mathematics) · See more »

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.

New!!: P versus NP problem and Graph isomorphism · See more »

Graph isomorphism problem

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

New!!: P versus NP problem and Graph isomorphism problem · See more »

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.

New!!: P versus NP problem and Halting problem · See more »

HP Labs

HP Labs is the exploratory and advanced research group for HP Inc. HP headquarters is in Palo Alto, California and has research and development facilities in Bristol, UK.

New!!: P versus NP problem and HP Labs · See more »

Independence (mathematical logic)

In mathematical logic, independence refers to the unprovability of a sentence from other sentences.

New!!: P versus NP problem and Independence (mathematical logic) · See more »

Information-theoretic security

Information-theoretic security is a cryptosystem whose security derives purely from information theory.

New!!: P versus NP problem and Information-theoretic security · See more »

Integer factorization

In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers.

New!!: P versus NP problem and Integer factorization · See more »

Integer programming

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.

New!!: P versus NP problem and Integer programming · See more »

Introduction to Algorithms

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

New!!: P versus NP problem and Introduction to Algorithms · See more »

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.

New!!: P versus NP problem and IP (complexity) · See more »

John Forbes Nash Jr.

John Forbes Nash Jr. (June 13, 1928 – May 23, 2015) was an American mathematician who made fundamental contributions to game theory, differential geometry, and the study of partial differential equations.

New!!: P versus NP problem and John Forbes Nash Jr. · See more »

John Markoff

John Gregory Markoff (born October 29, 1949) is a journalist best known for his work at The New York Times, and a book and series of articles about the 1990s pursuit and capture of hacker Kevin Mitnick.

New!!: P versus NP problem and John Markoff · See more »

John von Neumann

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

New!!: P versus NP problem and John von Neumann · See more »

Journal of Combinatorial Theory

The Journal of Combinatorial Theory, Series A and Series B, are mathematical journals specializing in combinatorics and related areas.

New!!: P versus NP problem and Journal of Combinatorial Theory · See more »

Journal of the Operational Research Society

The Journal of the Operational Research Society is a peer-reviewed academic journal covering operations research.

New!!: P versus NP problem and Journal of the Operational Research Society · See more »

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.

New!!: P versus NP problem and Karp's 21 NP-complete problems · See more »

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.

New!!: P versus NP problem and Knapsack problem · See more »

Kurt Gödel

Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.

New!!: P versus NP problem and Kurt Gödel · See more »

Lance Fortnow

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

New!!: P versus NP problem and Lance Fortnow · See more »

Latin square

In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column.

New!!: P versus NP problem and Latin square · See more »

László Babai

László "Laci" Babai (born July 20, 1950 in Budapest) from Babai's web site, retrieved 2016-01-28.

New!!: P versus NP problem and László Babai · See more »

Leonid Levin

Leonid Anatolievich Levin (Леони́д Анато́льевич Ле́вин; Леоні́д Анато́лійович Ле́він; born November 2, 1948) is a Soviet-American computer scientist.

New!!: P versus NP problem and Leonid Levin · See more »

Linear programming

Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

New!!: P versus NP problem and Linear programming · See more »

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.

New!!: P versus NP problem and List of NP-complete problems · See more »

List of unsolved problems in computer science

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

New!!: P versus NP problem and List of unsolved problems in computer science · See more »

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.

New!!: P versus NP problem and List of unsolved problems in mathematics · See more »

Martin Grötschel

Martin Grötschel (born 10 September 1948) is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, and operations research.

New!!: P versus NP problem and Martin Grötschel · See more »

Massachusetts Institute of Technology

The Massachusetts Institute of Technology (MIT) is a private research university located in Cambridge, Massachusetts, United States.

New!!: P versus NP problem and Massachusetts Institute of Technology · See more »

Michael O. Rabin

Michael Oser Rabin (מִיכָאֵל עוזר רַבִּין, born September 1, 1931) is an Israeli computer scientist and a recipient of the Turing Award.

New!!: P versus NP problem and Michael O. Rabin · See more »

Millennium Prize Problems

The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.

New!!: P versus NP problem and Millennium Prize Problems · See more »

MIT Press

The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States).

New!!: P versus NP problem and MIT Press · See more »

Moshe Vardi

Moshe Ya'akov Vardi (משה יעקב ורדי) is an Israeli mathematician and computer scientist.

New!!: P versus NP problem and Moshe Vardi · See more »

Multipartite graph

In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are or can be partitioned into k different independent sets.

New!!: P versus NP problem and Multipartite graph · See more »

National Security Agency

The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence.

New!!: P versus NP problem and National Security Agency · See more »

Natural proof

In computational complexity theory, a natural proof is a certain kind of proof establishing that one complexity class differs from another one.

New!!: P versus NP problem and Natural proof · See more »

Neil Immerman

Neil Immerman (24 November 1953, Manhasset, New York) is an American theoretical computer scientist, a professor of computer science at the University of Massachusetts Amherst.

New!!: P versus NP problem and Neil Immerman · See more »

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!!: P versus NP problem and New Year · See more »

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!!: P versus NP problem and New Year's Day · See more »

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.

New!!: P versus NP problem and New Year's Eve · See more »

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.

New!!: P versus NP problem and Non-deterministic Turing machine · See more »

NP (complexity)

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

New!!: P versus NP problem and NP (complexity) · See more »

NP-completeness

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

New!!: P versus NP problem and NP-completeness · See more »

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!!: P versus NP problem and NP-hardness · See more »

One-way function

In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input.

New!!: P versus NP problem and One-way function · See more »

Operations research

Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.

New!!: P versus NP problem and Operations research · See more »

Oracle machine

In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems.

New!!: P versus NP problem and Oracle machine · See more »

P (complexity)

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

New!!: P versus NP problem and P (complexity) · See more »

Peano axioms

In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

New!!: P versus NP problem and Peano axioms · See more »

Pearson Education

Pearson Education (see also Pearson PLC) is a British-owned education publishing and assessment service to schools and corporations, as well as directly to students.

New!!: P versus NP problem and Pearson Education · See more »

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.

New!!: P versus NP problem and PH (complexity) · See more »

Philosophy

Philosophy (from Greek φιλοσοφία, philosophia, literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.

New!!: P versus NP problem and Philosophy · See more »

Polymath Project

The Polymath Project is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution.

New!!: P versus NP problem and Polymath Project · See more »

Polynomial

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

New!!: P versus NP problem and Polynomial · See more »

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.

New!!: P versus NP problem and Polynomial hierarchy · See more »

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.

New!!: P versus NP problem and Polynomial-time reduction · See more »

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.

New!!: P versus NP problem and Presburger arithmetic · See more »

Princeton University

Princeton University is a private Ivy League research university in Princeton, New Jersey.

New!!: P versus NP problem and Princeton University · See more »

Protein structure prediction

Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its folding and its secondary and tertiary structure from its primary structure.

New!!: P versus NP problem and Protein structure prediction · See more »

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.

New!!: P versus NP problem and PSPACE · See more »

Public-key cryptography

Public-key cryptography, or asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner.

New!!: P versus NP problem and Public-key cryptography · See more »

Quantum algorithm

In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation.

New!!: P versus NP problem and Quantum algorithm · See more »

Quantum computing

Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.

New!!: P versus NP problem and Quantum computing · See more »

Randomized algorithm

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

New!!: P versus NP problem and Randomized algorithm · See more »

Reduction (complexity)

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

New!!: P versus NP problem and Reduction (complexity) · See more »

Rice University

William Marsh Rice University, commonly known as Rice University, is a private research university located on a 300-acre (121 ha) campus in Houston, Texas, United States.

New!!: P versus NP problem and Rice University · See more »

Richard Lipton

Richard Jay Lipton (born September 6, 1946) is an American-British computer scientist who has worked in computer science theory, cryptography, and DNA computing.

New!!: P versus NP problem and Richard Lipton · See more »

Robert M. Solovay

Robert Martin Solovay (born December 15, 1938) is an American mathematician specializing in set theory.

New!!: P versus NP problem and Robert M. Solovay · See more »

RSA (cryptosystem)

RSA (Rivest–Shamir–Adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission.

New!!: P versus NP problem and RSA (cryptosystem) · See more »

Russell Impagliazzo

Russell Impagliazzo is a professor of computer science at the University of California, San Diego.

New!!: P versus NP problem and Russell Impagliazzo · See more »

Scott Aaronson

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

New!!: P versus NP problem and Scott Aaronson · See more »

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.

New!!: P versus NP problem and Second-order logic · See more »

Sharp-P-complete

#P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory.

New!!: P versus NP problem and Sharp-P-complete · See more »

Shor's algorithm

Shor's algorithm, named after mathematician Peter Shor, is a quantum algorithm (an algorithm that runs on a quantum computer) for integer factorization formulated in 1994.

New!!: P versus NP problem and Shor's algorithm · See more »

SIAM Journal on Computing

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

New!!: P versus NP problem and SIAM Journal on Computing · See more »

Signature (logic)

In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language.

New!!: P versus NP problem and Signature (logic) · See more »

Simplex algorithm

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.

New!!: P versus NP problem and Simplex algorithm · See more »

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.

New!!: P versus NP problem and Stephen Cook · See more »

Steven Rudich

Steven Rudich (born October 4, 1961) is a professor in the Carnegie Mellon School of Computer Science.

New!!: P versus NP problem and Steven Rudich · See more »

String (computer science)

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.

New!!: P versus NP problem and String (computer science) · See more »

Subset sum problem

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

New!!: P versus NP problem and Subset sum problem · See more »

Sudoku

(originally called Number Place) is a logic-based, combinatorial number-placement puzzle.

New!!: P versus NP problem and Sudoku · See more »

Symmetric-key algorithm

Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext.

New!!: P versus NP problem and Symmetric-key algorithm · See more »

Symposium on Theoretical Aspects of Computer Science

Symposium on Theoretical Aspects of Computer Science (STACS) is an academic conference in the field of computer science.

New!!: P versus NP problem and Symposium on Theoretical Aspects of Computer Science · See more »

The New Yorker

The New Yorker is an American magazine of reportage, commentary, criticism, essays, fiction, satire, cartoons, and poetry.

New!!: P versus NP problem and The New Yorker · See more »

The Simpsons

The Simpsons is an American animated sitcom created by Matt Groening for the Fox Broadcasting Company.

New!!: P versus NP problem and The Simpsons · See more »

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.

New!!: P versus NP problem and Theoretical computer science · See more »

Theory of computation

In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm.

New!!: P versus NP problem and Theory of computation · See more »

Time complexity

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

New!!: P versus NP problem and Time complexity · See more »

Time hierarchy theorem

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

New!!: P versus NP problem and Time hierarchy theorem · See more »

Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.

New!!: P versus NP problem and Total order · See more »

Travelling Salesman (2012 film)

Travelling Salesman is a 2012 intellectual thriller film about four mathematicians solving the P versus NP problem, one of the most challenging mathematical problems in history.

New!!: P versus NP problem and Travelling Salesman (2012 film) · See more »

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.

New!!: P versus NP problem and Travelling salesman problem · See more »

Treehouse of Horror VI

"Treehouse of Horror VI" is the sixth episode of The Simpsons' seventh season and the sixth episode in the Treehouse of Horror series.

New!!: P versus NP problem and Treehouse of Horror VI · See more »

Triple DES

In cryptography, Triple DES (3DES), officially the Triple Data Encryption Algorithm (TDEA or Triple DEA), is a symmetric-key block cipher, which applies the DES cipher algorithm three times to each data block.

New!!: P versus NP problem and Triple DES · See more »

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.

New!!: P versus NP problem and Turing machine · See more »

Undecidable problem

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.

New!!: P versus NP problem and Undecidable problem · See more »

Unique games conjecture

In computational complexity theory, the unique games conjecture is a conjecture made by Subhash Khot in 2002.

New!!: P versus NP problem and Unique games conjecture · See more »

Universal quantification

In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".

New!!: P versus NP problem and Universal quantification · See more »

W. H. Freeman and Company

W.

New!!: P versus NP problem and W. H. Freeman and Company · See more »

Zermelo–Fraenkel set theory

In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.

New!!: P versus NP problem and Zermelo–Fraenkel set theory · See more »

2018

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

New!!: P versus NP problem and 2018 · See more »

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.

New!!: P versus NP problem and 2019 · See more »

Redirects here:

Algebrization, Complexity classes P and NP, NP = P, NP conjecture, NP problem, NP versus P problem, NP=P, NP=P problem, P = NP, P = NP problem, P = NP?, P = np, P ? NP, P Versus NP, P Versus NP Problem, P and NP, P conjecture, P is not NP, P v NP, P versus NP, P vs NP, P vs NP problem, P vs np, P vs. NP, P vs. NP problem, P ≟ NP, P ≠ NP, P!=NP, P/=NP, P/NP Problem, P==NP, P=?NP, P=NP, P=NP problem, P=NP?, P=np, P≟NP, P≠NP, Smale's third problem, Succinct problem, Succinct problems, Vinay Deolalikar, Vinay Deolilakar.

References

[1] https://en.wikipedia.org/wiki/P_versus_NP_problem

OutgoingIncoming
Hey! We are on Facebook now! »