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Encyclopedia of Algorithms pp 670–674Cite as

Exact Algorithms for General CNF SAT

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  • First Online:

  • 174 Accesses

Years and Authors of Summarized Original Work

  • 1998; Hirsch

  • 2003; Schuler

Problem Definition

The satisfiability problem (SAT) for Boolean formulas in conjunctive normal form (CNF) is one of the first NP-complete problems [2, 13]. Since its NP-completeness currently leaves no hope for polynomial-time algorithms, the progress goes by decreasing the exponent. There are several versions of this parametrized problem that differ in the parameter used for the estimation of the running time.

Problem 1 (SAT)

Input::

Formula F in CNF containing n variables, m clauses, and l literals in total.

Output::

“Yes” if F has a satisfying assignment, i.e., a substitution of Boolean values for the variables that makes F true. “No” otherwise.

The bounds on the running time of SAT algorithms can be thus given in the form \(\vert F\vert ^{O(1)} \cdot \alpha ^{n}\), | F | O(1) ⋅ βm, or \(\vert F\vert ^{O(1)} \cdot \gamma ^{l}\), where | F | is the length of a reasonable bit representation of F(i.e., the...

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Recommended Reading

  1. Calabro C, Impagliazzo R, Paturi R (2006) A duality between clause width and clause density for SAT. In: Proceedings of the 21st annual IEEE conference on computational complexity (CCC 2006), Prague. IEEE Computer Society, pp 252–260

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Author information

Authors and Affiliations

  1. Laboratory of Mathematical Logic, Steklov Institute of Mathematics, St. Petersburg, Russia

    Edward A. Hirsch

Authors
  1. Edward A. Hirsch
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Hirsch, E.A. (2016). Exact Algorithms for General CNF SAT. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_133

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