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Polynomial-time inference of all valid implications for Horn and related formulae

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Abstract

This paper investigates the complexity of a general inference problem: given a propositional formula in conjunctive normal form, find all prime implications of the formula. Here, a prime implication means a minimal clause whose validity is implied by the validity of the formula. We show that, under some reasonable assumptions, this problem can be solved in time polynomially bounded in the size of the input and in the number of prime implications. In the case of Horn formulae, the result specializes to yield an algorithm whose complexity grows only linearly with the number of prime implications. The result also applies to a class of formulae generalizing both Horn and quadratic formulae.

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Authors and Affiliations

  1. RUTCOR-Rutgers Center for Operations Research, Rutgers University, New Brunswick, NJ, USA

    E. Boros & P. L. Hammer

  2. Department of Quantitative Economics, University of Limburg, Maastricht, The Netherlands

    Y. Crama

Authors
  1. E. Boros
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  2. Y. Crama
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  3. P. L. Hammer
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To the memory of Robert G. Jeroslow

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Boros, E., Crama, Y. & Hammer, P.L. Polynomial-time inference of all valid implications for Horn and related formulae. Ann Math Artif Intell 1, 21–32 (1990). https://doi.org/10.1007/BF01531068

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  • DOI: https://doi.org/10.1007/BF01531068

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