Discrete relations on abstract simplicial complexes

On the one hand, a system of discrete relations is a generalization of cellular automaton and, on the other hand, it is a set-theoretical analog of a system of polynomial equations. An approach to studying such systems that is based on set-theoretical and topological constructs is considered. The proposed approach is implemented as a C program. Results of application of this approach to some binary cellular automata are given. In the binary case, cellular automata can be represented by systems of polynomial equations, which are normally studied by the Grobner basis method. Our approach is compared with this method on some examples.