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Simplifying interpreted formulas

  • D. W. Loveland
  • R. E. Shostak
Wednesday Morning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 87)

Abstract

A method is presented for converting a decision procedure for unquantified formulas in an arbitrary first-order theory to a simplifier for such formulas. Given a quantifier-free d.n.f. formula, the method produces a simplest (according to a given criterion) d.n.f. equivalent from among all formulas with atoms in the original formula. The method is predicated on techniques for minimizing purely boolean expressions in the presence of "don't-care" conditions. The don't-cares are used to capture the semantics of the interpreted literals in the formula to be simplified.

Two procedures are described: a primitive version of the method that advances the fundamental idea, and a more refined version intended for practical use. Complexity issues are discussed, as is a nontrivial example illustrating the utility of the method.

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6. References

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    Bartee, T. C., Lebow, J. L., Reed, I. S., Theory and Design of Digital Machines, McGraw-Hill, New York (1962).Google Scholar
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    Loveland, D. W., Shostak, R. E., "Simplifying Interpreted Expressions," to appear as SRI and IBM technical reports.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • D. W. Loveland
    • 1
  • R. E. Shostak
    • 2
  1. 1.Department of Computer ScienceDuke UniversityDurham
  2. 2.Computer Science Laboratory SRI InternationalMenlo Park

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