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

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.

• Type: Journal
• Year: 2008
• Where: JCSS
• Authors: Nadia Creignou, Phokion G. Kolaitis, Bruno Zanuttini
• Keywords: Boolean Relation, Conjunctive Query, JCSS 2008, Quadratic Algorithm