Sequentializing cellular automata

TL;DR

This paper characterizes which cellular automata can be implemented as a single reversible, left-to-right sweep without intermediate states, providing a decidable criterion for such sequentialization.

Contribution

It introduces a decidable characterization for sequentializing cellular automata as a reversible, single-pass process without intermediate states.

Findings

Identifies cellular automata that can be sequentialized in a single reversible sweep

Provides a decidable method to determine sequentializability

Characterizes the structure of automata compatible with this process

Abstract

We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be written as a single left-to-right sweep of a bijective rule from left to right over an infinite tape.