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Algorithms for the Satisfiability Problem

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Handbook of Combinatorial Optimization
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Abstract

This chapter discusses advances in SAT algorithm design, including the use of SAT algorithms as theory drivers, classic implementations of SAT solvers, and some theoretical aspects of SAT. Some applications to which SAT solvers have been successfully applied are also presented. The intention is to assist someone interested in applying SAT technology in solving some stubborn class of combinatorial problems.

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Notes

  1. 1.

    Each satisfiable set of Horn clauses has a unique minimal model with respect to 1, which can be computed in linear time by a well-known algorithm [53, 78] which is discussed in Sect. 6.2. Implications of the minimal model semantics may be found in Sect. 6.5, among others.

  2. 2.

    Horn formulas are solved efficiently (see Sect. 6.2).

  3. 3.

    Actual circuit voltage levels are abstracted to the values 0 and 1.

  4. 4.

    The meaning of ⇋ is given on Page 318.

  5. 5.

    See [39] for other results along these lines.

  6. 6.

    Random 3-SAT formulas are defined in Sect. 7, Page 440.

  7. 7.

    Finding inferences is referred to in the BDD literature as finding essential values to variables, and a set of inferences (a conjunction of literals) is referred to as a cube.

  8. 8.

    Random k-SAT formulas are defined in Sect. 7, Page 440.

  9. 9.

    Random k-SAT formulas are defined in Sect. 7, Page 440

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Acknowledgements

We thank John S. Schlipf for his help in writing some of the text, particularly the sections on the diagnosis of circuit faults and Binary Decision Diagrams. We especially appreciate John’s attention to detail which was quite valuable to us.

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Correspondence to John Franco or Sean Weaver .

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Franco, J., Weaver, S. (2013). Algorithms for the Satisfiability Problem. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_31

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