A note on decidability of cellularity

TL;DR

This paper proves that determining whether a regular language is cellular is decidable by leveraging a new characterization and a deep result from symbolic dynamics, advancing understanding of cellular automata languages.

Contribution

It introduces a decidability result for cellularity of regular languages using a novel characterization and symbolic dynamics insights.

Findings

Cellularity of regular languages is decidable.

A new characterization of cellular languages is established.

The proof relies on symbolic dynamics and a result by Boyle.

Abstract

A regular language L is said to be cellular if there exists a 1-dimensional cellular automaton CA such that L is the language consisting of the finite blocks associated with CA. It is shown that cellularity of a regular language is decidable using a new characterization of cellular languages formulated by Freiling, Goldstein and Moews and implied by a deep result of Boyle in symbolic dynamics.