Cellular Automata on Finite Monoids and Their Reversibility
Shuichi Inokuchi, Yuta Arima and Chihiro Iwanaga
We propose a framework for cellular automata (CAs) defined on finite monoids and investigate their reversibility properties, particularly focusing on those with linear local transition functions. Unlike traditional group-based models, the use of monoids allows for a broader class of transition dynamics. We derive necessary and sufficient conditions for reversibility in additive systems and provide theoretical and computational results that reveal the richness of reversible behavior in both uniform and non-uniform settings.
Keywords: Cellular automata, monoid, reversibility, additive system, linear rule, non-uniform CA
DOI: 10.32908/jca.v18.220626