Structure identification of Boolean relations and plain bases for co-clones

Authors:
Nadia Creignou;Phokion Kolaitis;Bruno Zanuttini
Affiliations:
LIF, UMR CNRS 6166, Université de la Méditerranée, 163, avenue de Luminy, 13 288 Marseille, France;IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120-6099, USA;GREYC, UMR CNRS 6072, Université de Caen, Boulevard du Maréchal Juin, 14032 Caen, France
Venue:
Journal of Computer and System Sciences
Year:
2008

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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.