On Residually Finite Semigroups of Cellullar Automata

TL;DR

This paper establishes an equivalence between the residual finiteness of a monoid and the monoid of all cellular automata over it with a finite alphabet, linking algebraic properties to automata theory.

Contribution

It proves that residual finiteness of a monoid is equivalent to that of the monoid of cellular automata over it with a finite alphabet.

Findings

Residual finiteness of monoids is characterized by cellular automata.

Equivalence established between monoid residual finiteness and automata residual finiteness.

Abstract

We prove that if $M$ is a monoid and $A$ a finite set with more than one element, then the residual finiteness of $M$ is equivalent to that of the monoid consisting of all cellular automata over $M$ with alphabet $A$.