Keywords and Synonyms
Constraint satisfaction
Problem Definition
This classic problem in complexity theory is concerned with efficiently finding a satisfying assignment to a propositional formula. The input is a formula with n Boolean variables which is expressed as an AND of ORs with 3 variables in each OR clause (a 3-CNF formula). The goal is to (1) find an assignment of variables to TRUE and FALSE so that the formula has value TRUE, or (2) prove that no such assignment exists. Historically, recognizing satisfiable 3-CNF formulas was the first “natural” example of an NP-complete problem, and, because it is NP-complete, no polynomial-time algorithm can succeed on all 3-CNF formulas unless P = NP [4,10]. Because of the numerous practical applications of 3-SAT, and also due to its position as the canonical NP-complete problem, many heuristic algorithms have been developed for solving3-SAT, and some of these algorithms have been analyzed rigorously on random instances.
Notation
A 3-CNF...
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Alon, N., Kahale, N.: A spectral technique for coloring random 3-colorable graphs. SIAM J. Comput. 26(6), 1733–1748 (1997)
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Flaxman, A. (2008). Random Planted 3-SAT. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_330
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