• problem be easy to solve? More unsolved problems in computer science The P versus NP problem is a major unsolved problem in theoretical computer science....
    63 KB (7,784 words) - 06:53, 25 April 2025
  • conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the...
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  • Thumbnail for NP-completeness
    in NP can be quickly solved—this is called the P versus NP problem. But if any NP-complete problem can be solved quickly, then every problem in NP can...
    30 KB (3,618 words) - 08:25, 21 May 2025
  • Thumbnail for Conjecture
    one of the Clay Mathematics Institute Millennium Prize Problems. The P versus NP problem is a major unsolved problem in computer science. Informally,...
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  • determine the practical limits on what computers can and cannot do. The P versus NP problem, one of the seven Millennium Prize Problems, is part of the field...
    50 KB (6,704 words) - 04:30, 7 July 2025
  • Thumbnail for NP (complexity)
    P   = ?   N P {\displaystyle {\mathsf {P\ {\overset {?}{=}}\ NP}}} More unsolved problems in computer science In computational complexity theory, NP (nondeterministic...
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  • Church–Turing thesis as having implications for the philosophy of mind. The P versus NP problem is an unsolved problem in computer science and mathematics. It...
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  • Thumbnail for Complexity class
    concerns whether P equals NP. The relationships between classes often answer questions about the fundamental nature of computation. The P versus NP problem, for...
    75 KB (10,382 words) - 17:19, 13 June 2025
  • most important open problems in theoretical computer science is the P versus NP problem, which (among other equivalent formulations) concerns the question...
    12 KB (1,626 words) - 23:58, 16 March 2025
  • the P versus NP problem, which is still widely considered the most important unsolved problem in theoretical computer science. The concept of NP-completeness...
    19 KB (2,354 words) - 04:22, 13 May 2025
  • co-NP; i.e., ⁠ co-NPNP {\displaystyle {\textsf {co-NP}}\subseteq {\textsf {NP}}} ⁠. Thus ⁠ co-NP = NP {\displaystyle {\textsf {co-NP}}={\textsf {NP}}}...
    7 KB (964 words) - 05:30, 9 May 2025
  • computationally intractable, and it drove interest in the study of NP-completeness and the P versus NP problem. Karp's 21 problems are shown below, many with their...
    5 KB (491 words) - 04:30, 25 May 2025
  • Aside, the P-NP Puzzler Has Consequences" The New York Times, October 7, 2009(subscription required) - L. Fortnow, "The Status of the P Versus NP Problem"...
    10 KB (1,054 words) - 18:14, 2 July 2025
  • #P-complete problem, if it existed, would solve the P versus NP problem by implying that P and NP are equal. No such algorithm is known, nor is a proof...
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  • (}n^{2^{100}}{\bigr )}} , although unusable in practice, would settle the P versus NP problem, considered the most important open problem in computer science...
    21 KB (2,636 words) - 22:36, 3 July 2025
  • Boolean satisfiability problem (category NP-complete problems)
    question of whether SAT has a polynomial-time algorithm would settle the P versus NP problem - one of the most important open problem in the theory of computing...
    45 KB (4,870 words) - 16:46, 24 June 2025
  • 2012 intellectual thriller film about four mathematicians who solve the P versus NP problem, one of the most challenging mathematical problems in history...
    7 KB (687 words) - 18:17, 24 November 2024
  • complexity P versus NP problem Termination analysis Worst-case execution time McConnell, Steve (2004). Code Complete (2nd ed.). Pearson Education. p. 374....
    53 KB (7,350 words) - 09:57, 12 June 2025
  • could solve, Kleitman and Bohman suggested the unsolved computer science P versus NP problem, but the film used other problems. The plot was inspired by George...
    65 KB (5,219 words) - 00:36, 9 July 2025
  • discrete mathematics solved in the second half of the 20th century. The P versus NP problem, which remains open to this day, is also important for discrete...
    163 KB (15,943 words) - 07:08, 3 July 2025
  • P ≠ NP, then for many important problems it is not only impossible to get an exact solution in polynomial time (as postulated by the P versus NP problem)...
    28 KB (3,066 words) - 07:53, 29 May 2025
  • efficient than known deterministic algorithms for many problems. The P versus NP problem encapsulates this conjectured greater efficiency available to...
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  • Thumbnail for Time complexity
    theory, the unsolved P versus NP problem asks if all problems in NP have polynomial-time algorithms. All the best-known algorithms for NP-complete problems...
    41 KB (4,997 words) - 15:01, 30 May 2025
  • techniques that are not affected by relativization cannot resolve the P versus NP problem. Another technique is the proof of completeness for a complexity...
    29 KB (3,915 words) - 00:22, 27 June 2025
  • when experts in the field disagree about proposed solutions. P versus NP problem – The P vs NP problem is a major unsolved question in computer science that...
    10 KB (1,167 words) - 06:45, 24 June 2025
  • PNP (redirect from PnP)
    phosphorylase, an enzyme 4-Nitrophenol or p-nitrophenol Pyridoxine phosphate, a form of vitamin B6 PNP transistor P versus NP problem Plug and play, not requiring...
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  • Thumbnail for Algorithm
    fastest algorithm for some problems is an open question known as the P versus NP problem. There are two large classes of such algorithms: Monte Carlo...
    61 KB (7,009 words) - 22:21, 2 July 2025
  • Thumbnail for Gödel Prize
    the first to mention the "P versus NP" question, in a 1956 letter to John von Neumann in which Gödel asked whether a certain NP-complete problem could be...
    31 KB (2,200 words) - 21:16, 23 June 2025
  • relevant to the P versus NP problem and their impact on computational complexity theory. Although some of the general problems are #P-hard problems, the...
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  • that Np for a curve E with rank r obeys an asymptotic law ∏ p ≤ x N p p ≈ C log ⁡ ( x ) r  as  x → ∞ {\displaystyle \prod _{p\leq x}{\frac {N_{p}}{p}}\approx...
    25 KB (3,131 words) - 13:57, 7 June 2025