Formal Logic of Cellular Automata

Abstract

This paper develops a formal logic, named L-CA, targeting modeling of one-dimensional binary cellular automata. We first develop the syntax of L-CA, then give semantics to L-CA in the domain of all binary strings. Then the elementary cellular automata and four-neighborhood binary cellular automata are shown as models of the logic. These instances point out that there are other models of L-CA. Finally it is proved that any one-dimensional binary cellular automaton is a model of the proposed logic.