Time-Symmetric Cellular Automata

TL;DR

This paper formalizes the concept of time-symmetry in cellular automata, exploring its theoretical foundations and relations to reversibility, and highlights open problems for future research in discrete dynamical systems.

Contribution

It introduces a formal framework for time-symmetry in cellular automata, connecting it with reversibility and proposing open problems for further investigation.

Findings

Established basic facts about time-symmetry in cellular automata

Connected time-symmetry with reversibility in discrete systems

Outlined open problems to guide future research

Abstract

Together with the concept of reversibility, another relevant physical notion is time-symmetry, which expresses that there is no way of distinguishing between backward and forward time directions. This notion, found in physical theories, has been neglected in the area of discrete dynamical systems. Here we formalize it in the context of cellular automata and establish some basic facts and relations. We also state some open problems that may encourage further research on the topic.