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

Nadia Creignou (1) , Phokion G. Kolaitis (2) , Bruno Zanuttini (3)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille
2 CPSC - Department of Computer Science [Calgary]
3 Equipe MAD - Laboratoire GREYC - UMR6072

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.

Domaines: Intelligence artificielle [cs.AI]

Nadia Creignou, Phokion G. Kolaitis, Bruno Zanuttini. Structure Identification of Boolean Relations and Plain Bases for co-Clones. Journal of Computer and System Sciences, 2008, 74 (7), pp.1103-1115. ⟨hal-00995233⟩