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In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete. That is, it is in NP , and any problem in NP can be reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem.
The concept of NP-completeness was introduced in 1971 (see Cook–Levin theorem), though the term NP-complete was introduced later. At the 1971 STOC conference, there was a fierce debate between the computer scientists about whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine.
Schaefer's dichotomy theorem states that, for any restriction to Boolean functions that can be used to form these subformulas, the corresponding satisfiability problem is in P or NP-complete. The membership in P of the satisfiability of 2CNF, Horn, and XOR-SAT formulae are special cases of this theorem. [14]
This theorem was proven independently by Leonid Levin in the Soviet Union, and has thus been given the name the Cook–Levin theorem. The paper also formulated the most famous problem in computer science, the P vs. NP problem. Informally, the "P vs. NP" question asks whether every optimization problem whose answers can be efficiently verified ...
Conway circle theorem (Euclidean plane geometry) Cook's theorem (computational complexity theory) Corners theorem (arithmetic combinatorics) Corona theorem (complex analysis) Courcelle's theorem (graph theory) Cousin's lemma (real analysis) Cox's theorem (probability) Craig's theorem (mathematical logic) Craig's interpolation theorem ...
Sometimes the following alternative definition is considered: a pps is given as a proof-verification algorithm P(A,x) with two inputs. If P accepts the pair (A,x) we say that x is a P-proof of A. P is required to run in polynomial time, and moreover, it must hold that A has a P-proof if and only if it is a tautology.
The Mind Doesn't Work That Way: The Scope and Limits of Computational Psychology. Cambridge, MA and London: The MIT Press. ISBN 9780262062121. OCLC 43109956. Fodor, Jerry (2010). LOT 2: The Language of Thought Revisited. Oxford and New York: Oxford University Press. ISBN 9780199548774. OCLC 470698989. Harnad, Stevan (1994). "Computation Is Just ...
The circuit on the left is satisfiable but the circuit on the right is not. In theoretical computer science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean circuit has an assignment of its inputs that makes the output true. [1]