Geodesic
On $m$-junctive predicates on a finite set
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 3, pp. 46-59

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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. Bibliogr. 15.
Keywords: predicate on a finite set, function on a finite set, near-unanimity function, bijunctive predicate, $m$-junctive predicate, conjunctive normal form, generalized satisfiability problem. 
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     author = {S. N. Selezneva},
     title = {On $m$-junctive predicates on a finite set},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {46--59},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2019_26_3_a2/}
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S. N. Selezneva. On $m$-junctive predicates on a finite set. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 3, pp. 46-59. http://geodesic.mathdoc.fr/item/DA_2019_26_3_a2/