Exclusive and essential sets of implicates of a Boolean function
(joint work with Endre Boros, Alex Kogan, Petr Kucera and Petr Savicky)
Abstract: In this talk we shall study relationships between CNF representations of a given Boolean function f and certain sets of implicates of f. We introduce two definitions of sets of implicates which are both based on the properties of resolution. The first type of sets, called exclusive sets of implicates, is shown to have a functional property useful for decompositions. The second type of sets, called essential sets of implicates, is proved to possess an orthogonality property, which implies that every CNF representation and every essential set must intersect. The latter property then leads to many interesting consequences, which we plan to discuss in the talk.