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Simplifying interpreted formulas

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5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980 (CADE 1980)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 87))

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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.

Supported in part by AFOSR Contract F49620-79-C-0099

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6. References

  1. Bartee, T. C., Lebow, J. L., Reed, I. S., Theory and Design of Digital Machines, McGraw-Hill, New York (1962).

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  2. Loveland, D. W., Shostak, R. E., "Simplifying Interpreted Expressions," to appear as SRI and IBM technical reports.

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  3. McCluskey, E. J., "Minimization of Boolean Functions," Bell System Tech. Journal, Vol. 35, pp. 1417–1444 (Nov. 1956).

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Author information

Authors and Affiliations

  1. Department of Computer Science, Duke University, 27706, Durham, North Carolina

    D. W. Loveland

  2. Computer Science Laboratory SRI International, 94025, Menlo Park, California

    R. E. Shostak

Authors
  1. D. W. Loveland
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  2. R. E. Shostak
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Editor information

Wolfgang Bibel Robert Kowalski

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© 1980 Springer-Verlag Berlin Heidelberg

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Loveland, D.W., Shostak, R.E. (1980). Simplifying interpreted formulas. In: Bibel, W., Kowalski, R. (eds) 5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980. CADE 1980. Lecture Notes in Computer Science, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10009-1_9

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  • DOI: https://doi.org/10.1007/3-540-10009-1_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10009-6

  • Online ISBN: 978-3-540-38140-2

  • eBook Packages: Springer Book Archive

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