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P versus NP problem

Index P versus NP problem

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

Table of Contents

  1. 159 relations: ACM SIGACT, Addison-Wesley, Advanced Encryption Standard, AKS primality test, Alexander Razborov, Algorithm, Algorithmic efficiency, Anil Nerode, Annals of Mathematics, Arithmetic, Artificial intelligence, Association for Computing Machinery, Average-case complexity, Avi Wigderson, Aviezri Fraenkel, Big O notation, Bitcoin, Black box, Blockchain, Boolean satisfiability problem, Cambridge University Press, 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, Cryptocurrency, Cryptographic hash function, Cryptography, David Eppstein, Decision problem, Descriptive complexity theory, Deterministic automaton, Discrete logarithm, DLIN, Donald Knuth, Economics, Elementary (TV series), Encyclopædia Britannica, Entscheidungsproblem, EXPTIME, ... Expand index (109 more) »

  2. 1956 in computing
  3. Computer-related introductions in 1956
  4. Millennium Prize Problems
  5. Structural complexity theory
  6. Unsolved problems 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.

See P versus NP problem and ACM SIGACT

Addison-Wesley

Addison–Wesley is an American publisher of textbooks and computer literature.

See P versus NP problem and Addison-Wesley

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.

See P versus NP problem and Advanced Encryption Standard

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 an article titled "PRIMES is in P".

See P versus NP problem and AKS primality test

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.

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Algorithm

In mathematics and computer science, an algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation.

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Algorithmic efficiency

In computer science, algorithmic efficiency is a property of an algorithm which relates to the amount of computational resources used by the algorithm.

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Anil Nerode

Anil Nerode (born 1932) is an American mathematician, known for his work in mathematical logic and for his many-decades tenure as a professor at Cornell University.

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Annals of Mathematics

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

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Arithmetic

Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division.

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Artificial intelligence

Artificial intelligence (AI), in its broadest sense, is intelligence exhibited by machines, particularly computer systems.

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Association for Computing Machinery

The Association for Computing Machinery (ACM) is a US-based international learned society for computing.

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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.

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Avi Wigderson

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

See P versus NP problem and Avi Wigderson

Aviezri Fraenkel

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

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Big O notation

Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity.

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Bitcoin

Bitcoin (abbreviation: BTC; sign: ₿) is the first decentralized cryptocurrency.

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Black box

In science, computing, and engineering, a black box is a system which can be viewed in terms of its inputs and outputs (or transfer characteristics), without any knowledge of its internal workings.

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Blockchain

A blockchain is a distributed ledger with growing lists of records (blocks) that are securely linked together via cryptographic hashes.

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Boolean satisfiability problem

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

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Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

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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.

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Chess

Chess is a board game for two players.

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Clay Mathematics Institute

The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge.

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Co-NP

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

See P versus NP problem and Co-NP

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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Cobham's thesis

Cobham's thesis, also known as Cobham–Edmonds thesis (named after Alan Cobham and Jack Edmonds),.

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Complexity class

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

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Composite number

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

See P versus NP problem and Composite number

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other.

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Computer programming

Computer programming or coding is the composition of sequences of instructions, called programs, that computers can follow to perform tasks.

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Computer science

Computer science is the study of computation, information, and automation.

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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.

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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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Cornell University

Cornell University is a private Ivy League land-grant research university based in Ithaca, New York.

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Cryptocurrency

A cryptocurrency, crypto-currency, or crypto is a digital currency designed to work as a medium of exchange through a computer network that is not reliant on any central authority, such as a government or bank, to uphold or maintain it.

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Cryptographic hash function

A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with a fixed size of n bits) that has special properties desirable for a cryptographic application.

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Cryptography

Cryptography, or cryptology (from κρυπτός|translit.

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David Eppstein

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

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Decision problem

In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values.

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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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Deterministic automaton

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

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Discrete logarithm

In mathematics, for given real numbers a and b, the logarithm logb a is a number x such that. P versus NP problem and Discrete logarithm are unsolved problems in computer science.

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DLIN

In computational complexity theory, DLIN is the class of decision problems that can be solved by a multitape Turing machine in linear time, O(n). P versus NP problem and DLIN are Structural complexity theory.

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Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist and mathematician.

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Economics

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

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Elementary (TV series)

Elementary is an American procedural drama television series that presented a contemporary update of Sir Arthur Conan Doyle's character Sherlock Holmes.

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Encyclopædia Britannica

The British Encyclopaedia is a general knowledge English-language encyclopaedia.

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Entscheidungsproblem

In mathematics and computer science, the paren) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers an inputted statement and answers "yes" or "no" according to whether it is universally valid, i.e., valid in every structure.

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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 that are solvable by a deterministic Turing machine in exponential time, i.e., in O(2p(n)) time, where p(n) is a polynomial function of n. EXPTIME is one intuitive class in an exponential hierarchy of complexity classes with increasingly more complex oracles or quantifier alternations.

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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.

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First-order logic

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

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Fixed-point combinator

In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator), is a higher-order function (i.e. a function which takes a function as argument) that returns some ''fixed point'' (a value that is mapped to itself) of its argument function, if one exists.

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Game complexity

Combinatorial game theory measures game complexity in several ways.

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Game theory

Game theory is the study of mathematical models of strategic interactions.

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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.

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Gerhard J. Woeginger

Gerhard J. Woeginger (31 May 1964 – 1 April 2022) was an Austrian mathematician and computer scientist who worked in Germany as a professor at RWTH Aachen University, where he chaired the algorithms and complexity group in the department of computer science.

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Graph (discrete mathematics)

In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related".

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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 f(u) and f(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. P versus NP problem and graph isomorphism problem are unsolved problems in computer science.

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Graph minor

In graph theory, an undirected graph is called a minor of the graph if can be formed from by deleting edges, vertices and by contracting edges.

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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, or continue to run forever.

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Hilbert's tenth problem

Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900.

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Independence (mathematical logic)

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

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Information-theoretic security

A cryptosystem is considered to have information-theoretic security (also called unconditional security) if the system is secure against adversaries with unlimited computing resources and time.

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Integer factorization

In number theory, integer factorization is the decomposition of a positive integer into a product of integers. P versus NP problem and integer factorization are unsolved problems in computer science.

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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.

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IP (complexity)

In computational complexity theory, the class IP (interactive proof) is the class of problems solvable by an interactive proof system.

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John Forbes Nash Jr.

John Forbes Nash, Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations.

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John Markoff

John Gregory Markoff (born October 24, 1949) is a journalist best known for his work covering technology at The New York Times for 28 years until his retirement in 2016, and a book and series of articles about the 1990s pursuit and capture of hacker Kevin Mitnick.

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John von Neumann

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

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Journal of Combinatorial Theory

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

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Journal of the Operational Research Society

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

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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 is the following problem in combinatorial optimization: It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.

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Knuth's up-arrow notation

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.

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Kurt Gödel

Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher.

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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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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.

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László Babai

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

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Leonid Levin

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

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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 and objective are represented by linear relationships.

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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 notable unsolved problems in computer science. P versus NP problem and list of unsolved problems in computer science are conjectures and unsolved problems in computer science.

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List of unsolved problems in mathematics

Many mathematical problems have been stated but not yet solved. P versus NP problem and List of unsolved problems in mathematics are conjectures and unsolved problems in mathematics.

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Michael J. Fischer

Michael John Fischer (born 1942) is an American computer scientist who works in the fields of distributed computing, parallel computing, cryptography, algorithms and data structures, and computational complexity.

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Michael O. Rabin

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

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Millennium Prize Problems

The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. P versus NP problem and Millennium Prize Problems are unsolved problems in mathematics.

See P versus NP problem and Millennium Prize Problems

MIT Press

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

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Moshe Vardi

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

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Multipartite graph

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

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National Security Agency

The National Security Agency (NSA) is an intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI).

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Natural proof

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

See P versus NP problem and Natural proof

NLIN

In computational complexity theory, NLIN is the class of decision problems that can be solved by a nondeterministic multitape Turing machine in linear time, O(n). P versus NP problem and NLIN are Structural complexity theory.

See P versus NP problem and NLIN

Nondeterministic Turing machine

In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations.

See P versus NP problem and Nondeterministic Turing machine

NP (complexity)

In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.

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NP-completeness

In computational complexity theory, a problem is NP-complete when. P versus NP problem and NP-completeness are mathematical optimization.

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NP-hardness

In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a solution for H takes 1 unit time, Hs solution can be used to solve L in polynomial time.

See P versus NP problem and NP-hardness

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. P versus NP problem and one-way function are unsolved problems in computer science.

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Operations research

Operations research (operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making.

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Oracle machine

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

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P (complexity)

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

See P versus NP problem and P (complexity)

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.

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Pearson Education

Pearson Education, known since 2011 as simply Pearson, is the educational publishing and services subsidiary of the international corporation Pearson plc.

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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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Philosophy

Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language.

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Polynomial

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.

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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 NP and co-NP. P versus NP problem and polynomial hierarchy are Structural complexity theory.

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Polynomial-time reduction

In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another.

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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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Princeton University

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

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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 secondary and tertiary structure from primary structure.

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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.

See P versus NP problem and PSPACE

Public-key cryptography

Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys.

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Quantum algorithm

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

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Quantum complexity theory

Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics.

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Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena.

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Quasi-polynomial time

In computational complexity theory and the analysis of algorithms, an algorithm is said to take quasi-polynomial time if its time complexity is quasi-polynomially bounded.

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R (complexity)

In computational complexity theory, R is the class of decision problems solvable by a Turing machine, which is the set of all recursive languages (also called decidable languages).

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Randomized algorithm

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

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RE (complexity)

In computability theory and computational complexity theory, RE (recursively enumerable) is the class of decision problems for which a 'yes' answer can be verified by a Turing machine in a finite amount of time.

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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. P versus NP problem and reduction (complexity) are Structural complexity theory.

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Rice University

Rice University, formally William Marsh Rice University, is a private research university in Houston, Texas, United States.

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Richard E. Ladner

Richard Emil Ladner is an American computer scientist known for his contributions to both theoretical computer science and assistive technology.

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Robert M. Solovay

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

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RSA (cryptosystem)

RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem, one of the oldest widely used for secure data transmission.

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Russell Impagliazzo

Russell Graham Impagliazzo is a professor of computer science at the University of California, San Diego, specializing in computational complexity theory.

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Scientific American

Scientific American, informally abbreviated SciAm or sometimes SA, is an American popular science magazine.

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Scott Aaronson

Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and Schlumberger Centennial Chair of Computer Science at the University of Texas at Austin.

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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.

See P versus NP problem and Second-order logic

Shor's algorithm

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer.

See P versus NP problem and Shor's algorithm

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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Signature (logic)

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

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Simplex algorithm

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

See P versus NP problem and Simplex algorithm

Stephen Cook

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

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Steven Rudich

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

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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.

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Subset sum problem

The subset sum problem (SSP) is a decision problem in computer science.

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Sudoku

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

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Symmetric-key algorithm

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

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The Simpsons

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

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Theoretical computer science

Theoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation.

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Theory of computation

In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones).

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Time complexity

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

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Time hierarchy theorem

In computational complexity theory, the time hierarchy theorems are important statements about time-bounded computation on Turing machines. P versus NP problem and time hierarchy theorem are Structural complexity theory.

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Total order

In mathematics, a total order or linear order is a partial order in which any two elements are comparable.

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Travelling Salesman (2012 film)

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

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Travelling salesman problem

The travelling salesman problem, also known as the travelling salesperson 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 exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research.

See P versus NP problem and Travelling salesman problem

Treehouse of Horror VI

"Treehouse of Horror VI" is the sixth episode of the seventh season of the American animated television series The Simpsons, and the sixth episode in the Treehouse of Horror series.

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Triple DES

In cryptography, Triple DES (3DES or TDES), 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.

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Turing machine

A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules.

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Undecidable problem

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

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Unique games conjecture

In computational complexity theory, the unique games conjecture (often referred to as UGC) is a conjecture made by Subhash Khot in 2002. P versus NP problem and unique games conjecture are conjectures and unsolved problems in computer science.

See P versus NP problem and Unique games conjecture

Universal quantification

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

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University of Texas at Austin

The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas.

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UP (complexity)

In complexity theory, UP (unambiguous non-deterministic polynomial-time) is the complexity class of decision problems solvable in polynomial time on an unambiguous Turing machine with at most one accepting path for each input.

See P versus NP problem and UP (complexity)

William Gasarch

William Ian Gasarch (born 1959) is an American computer scientist known for his work in computational complexity theory, computability theory, computational learning theory, and Ramsey theory.

See P versus NP problem and William Gasarch

YouTube

YouTube is an American online video sharing platform owned by Google.

See P versus NP problem and YouTube

Zermelo–Fraenkel set theory

In set theory, 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.

See P versus NP problem and Zermelo–Fraenkel set theory

See also

1956 in computing

Computer-related introductions in 1956

Millennium Prize Problems

Structural complexity theory

Unsolved problems in computer science

References

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

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

, 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, Graph minor, Halting problem, Hilbert's tenth problem, Independence (mathematical logic), Information-theoretic security, Integer factorization, Integer programming, 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, Knuth's up-arrow notation, 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, Michael J. Fischer, Michael O. Rabin, Millennium Prize Problems, MIT Press, Moshe Vardi, Multipartite graph, National Security Agency, Natural proof, NLIN, Nondeterministic Turing machine, NP (complexity), NP-completeness, NP-hardness, One-way function, Operations research, Oracle machine, P (complexity), Peano axioms, Pearson Education, PH (complexity), Philosophy, Polynomial, Polynomial hierarchy, Polynomial-time reduction, Presburger arithmetic, Princeton University, Protein structure prediction, PSPACE, Public-key cryptography, Quantum algorithm, Quantum complexity theory, Quantum computing, Quasi-polynomial time, R (complexity), Randomized algorithm, RE (complexity), Reduction (complexity), Rice University, Richard E. Ladner, Robert M. Solovay, RSA (cryptosystem), Russell Impagliazzo, Scientific American, Scott Aaronson, Second-order logic, 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, 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, University of Texas at Austin, UP (complexity), William Gasarch, YouTube, Zermelo–Fraenkel set theory.