A characterization of the reversibility of linear cellular automata

2026-08-20

AI Summary

本文解决了线性细胞自动机可逆性的问题，通过证明在特定条件下存在双射线性细胞自动机其逆不是细胞自动机。

Abstract

Let $G$ be a group, let $\mathbb{K}$ be a field, and let $V$ be a $\mathbb{K}$-vector space. We prove that there exists a bijective linear cellular automaton $V^G\to V^G$ whose inverse is not a cellular automaton if and only if $G$ is not locally finite and $\dim_{\mathbb{K}}V \geq |\mathbb{K}|^{\aleph_0}$. This answers an open problem proposed by T. Ceccherini-Silberstein and M. Coornaert.

Problem

• linear cellular automata
• reversibility
• bijective

Innovation

• linear cellular automata
• reversibility
• bijective