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International Conference on Artificial Intelligence: Methodology, Systems, and Applications

AIMSA 2018: Artificial Intelligence: Methodology, Systems, and Applications pp 228–239Cite as

Approaches for Enumerating All the Essential Prime Implicants

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11089))

Abstract

The aim of this paper is to study the problem of enumerating all the essential prime implicants (EPIes) of a CNF formula. We first provide some interesting computational complexity results. We show in particular that the problem of checking whether a prime implicant of a CNF formula is essential is NP-complete. Then, we propose a simple characterization of the e-models of a CNF formula. An e-model is a model covered by a unique prime implicant, which is necessarily essential. Our characterization is then used to define a linear-time algorithm for checking whether a model of CNF formula is an e-model or not. Finally, using our characterization of the e-models, we propose two approaches for enumerating all the EPIes of a CNF formula.

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Authors and Affiliations

  1. CRIL-CNRS, Université d’Artois, 62307, Lens Cedex, France

    Yakoub Salhi

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  1. Yakoub Salhi
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Correspondence to Yakoub Salhi .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Gennady Agre

  2. Universität des Saarlandes, Saarbrücken, Germany

    Josef van Genabith

  3. DFKI GmbH, Saarbrücken, Germany

    Thierry Declerck

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Salhi, Y. (2018). Approaches for Enumerating All the Essential Prime Implicants. In: Agre, G., van Genabith, J., Declerck, T. (eds) Artificial Intelligence: Methodology, Systems, and Applications. AIMSA 2018. Lecture Notes in Computer Science(), vol 11089. Springer, Cham. https://doi.org/10.1007/978-3-319-99344-7_21

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  • DOI: https://doi.org/10.1007/978-3-319-99344-7_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99343-0

  • Online ISBN: 978-3-319-99344-7

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