Structure Identification of Boolean Relations and Plain Bases for co-Clones

Abstract : We give a quadratic algorithm for the following structure identification problem: given a Boolean relation R and a finite set S of Boolean relations, can the relation R be expressed as a conjunctive query over the relations in the set S? Our algorithm is derived by first introducing the concept of a plain basis for a co-clone and then identifying natural plain bases for every co-clone in Post's lattice. In the process, we also give a quadratic algorithm for the problem of finding the smallest co-clone containing a Boolean relation.
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Nadia Creignou, Phokion G. Kolaitis, Bruno Zanuttini. Structure Identification of Boolean Relations and Plain Bases for co-Clones. Journal of Computer and System Sciences, Elsevier, 2008, 74 (7), pp.1103-1115. ⟨hal-00995233⟩

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