Abstract
We consider predicates on finite sets. The predicates invariant under some (m + 1)-ary near-unanimity function are called m-junctive. We propose to represent the predicates on a finite set in generalized conjunctive normal forms (GCNFs). The properties for GCNFs of m-junctive predicates are obtained. We prove that each m-junctive predicate can be represented by a strongly consistent GCNF in which every conjunct contains at most m variables. This representation of an m-junctive predicate is called reduced. Some fast algorithm is proposed for finding a reduced representation for an m-junctive predicate. It is shown how the obtained properties of GCNFs of m-junctive predicates can be applied for constructing a fast algorithm for the generalized S-satisfiability problem in the case that S contains only the predicates invariant under a common near unanimity function.
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Funding
The author was supported by Russian Foundation for Basic Research (project no. 17-01-00782-a).
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Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 3, pp. 46–59.
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Selezneva, S.N. On m-Junctive Predicates on a Finite Set. J. Appl. Ind. Math. 13, 528–535 (2019). https://doi.org/10.1134/S199047891903013X
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DOI: https://doi.org/10.1134/S199047891903013X