On Compatibility of Discrete Relations

Abstract

An approach to compatibility analysis of systems of discrete relations is proposed. Unlike the Groebner basis technique, the proposed scheme is not based on the polynomial ring structure. It uses more primitive set-theoretic and topological concepts and constructions. We illustrate the approach by application to some two-state cellular automata. In the two-state case the Groebner basis method is also applicable, and we compare both approaches.