Abstract
The local function of a cellular automaton with binary states can be expressed by a formula in propositional logic. If it is of a reversible cellular automaton, its inverse transition function can also be expressed by some formula in propositional logic, and there exists a cellular automaton defined by it as a local function. The local function of the composition of two cellular automata can be created by multiplication of these formulae in propositional logic.In this paper, we deal with logical formulae on a commutative monoid as local functions of elementary cellular automata. We discuss the commutativity of multiplication of formulae and show some condition for formulae to satisfy the commutativity of the composition of some elementary cellular automata.
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