P versus NP problem

Definition

The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.

Related concepts

2-EXPTIME AC0 ACC0 AKS primality test ALL (complexity)APX Addison-Wesley Advanced Encryption Standard Alexander Razborov Algorithm Algorithmic efficiency Anil Nerode Annals of Mathematics Arithmetic Arithmetic circuit complexity Arithmetical hierarchy Arthur–Merlin protocol Artificial intelligence Association for Computing Machinery Average-case complexity Avi Wigderson Aviezri Fraenkel BPP (complexity)BQP Big O notation Birch and Swinnerton-Dyer conjecture Bitcoin Black box Blockchain Bonnie Berger Boolean hierarchy Boolean satisfiability problem Bruce Reed (mathematician)CC (complexity)Cambridge University Press Certificate (complexity)Chess Christos Papadimitriou Clay Math Institute Clay Mathematics Institute Co-NP Co-NP-complete Cobham's thesis Complexity class Composite number Computational complexity theory Computational theory Computer programming Computer science Computers and Intractability Cook–Levin theorem Cornell University Cryptocurrency Cryptographic hash function Cryptography Curve fitting DLIN DLOGTIME DSPACE DTIME David Eppstein David S. Johnson Decision problem Descriptive complexity Deterministic Turing machine Deterministic computation Discrete logarithm problem Donald Knuth ELEMENTARY EXPSPACE EXPTIME Economics Elementary (TV series)Encyclopædia Britannica Entscheidungsproblem Euler diagram Exponential hierarchy Exponential time Exponential time hypothesis F. Thomson Leighton FL (complexity)FNP (complexity)FPT (class)FP (complexity)Fermat's Last Theorem First-order logic Fixed-point combinator Game theory General number field sieve Gerhard J. Woeginger Graph (discrete mathematics)Graph isomorphism Graph isomorphism problem Graph minor Grzegorczyk hierarchy Halting problem Hilbert's tenth problem Hodge conjecture IP (complexity)Independence (mathematical logic)InformIT (publisher)Information-theoretic security Integer factorization problem Integer programming Interactive proof system Introduction to Algorithms John Forbes Nash Jr.John Markoff John von Neumann Journal of Combinatorial Theory Journal of the ACM Journal of the Operational Research Society Karp's 21 NP-complete problems Knapsack problem Knuth's up-arrow notation Kurt Gödel L (complexity)Lance Fortnow Latin square Leonid Levin Linear order Linear programming Linear time List of Elementary episodes List of NP-complete problems List of complexity classes List of unsolved problems in computer science List of unsolved problems in mathematics László Babai MIT Press Martin Grötschel Michael Garey Michael J. Fischer Michael O. Rabin Millennium Prize Problems Moshe Y. Vardi Multipartite graph NC (complexity)NEXPTIME NL-complete NLIN NL (complexity)NONELEMENTARY NP-completeness NP-hard NP-hardness NP-intermediate NP (complexity)NSPACE NTIME National Security Agency Natural proof Navier–Stokes existence and smoothness Neil Immerman Non-constructive proof Non-deterministic Turing machine Nondeterministic Turing machine Oded Goldreich One-way functions Operations research Oracle machine P-complete PH (complexity)PP (complexity)PR (complexity)PSPACE PSPACE-complete P (complexity)Parameterized complexity Parity P Peano axioms Philosophy Poincaré conjecture PolyL Polynomial Polynomial-time many-one reduction Polynomial function Polynomial hierarchy Polynomial time Polynomial time hierarchy Presburger arithmetic Prime factorization Princeton University Probabilistically checkable proof Protein structure prediction Public-key cryptography QMA Quadratic time Quantum algorithm Quantum complexity theory Quantum computation Quasi-polynomial time RE (complexity)RL (complexity)RP (complexity)RSA (algorithm)R (complexity)Randomized algorithm Reduction (complexity)Relativizing proof Rice University Richard E. Ladner Riemann hypothesis Robert M. Solovay Russell Impagliazzo SC (complexity)SIAM Journal on Computing SIGACT News SL (complexity)Scientificamerican.com Scott Aaronson Second-order logic Sharp-P Sharp-P-complete Shor's algorithm Signature (logic)Simplex algorithm Stephen Cook Steven Rudich String (computer science)Subset sum problem Sudoku Symmetric cipher TC0 TC (complexity)TFNP The Simpsons Theoretical computer science Theory of computation Thomas Cormen Time complexity Time hierarchy theorem Traveling salesman problem Travelling Salesman (2012 film)Travelling salesman problem Treehouse of Horror VI Triple DES Turing machine UP (complexity)UT Austin Undecidable problem Unique games conjecture Universal quantification Upper bound Uwe Schöning W. H. Freeman and Company W Hierarchy William Gasarch Yang–Mills existence and mass gap YouTube ZFC ZPP (complexity)≠♯P ♯P-complete

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