On Compatibility of Discrete Relations

TL;DR

This paper introduces a set-theoretic and topological approach to analyzing the compatibility of discrete relations, offering an alternative to Groebner basis methods, and demonstrates its application to two-state cellular automata.

Contribution

It presents a novel compatibility analysis method for discrete relations that does not rely on polynomial algebra, contrasting it with existing Groebner basis techniques.

Findings

The proposed method effectively analyzes compatibility in discrete systems.

Comparison shows advantages over Groebner basis in certain cases.

Application to cellular automata demonstrates practical utility.

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.