2022/01/31 by Xuan Kien Phung, Phung, Xuan Kien
Computer Science · #05C25 #20F69 #37B10 #37B15 #37B51 #68Q80 #Cellular Automata and Applications #Coding theory and cryptography #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2201.13283
openalex publication_date 2022/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable injectivity, stable reversibility, stable post-surjectivity and investigate several dynamical properties of such automata. In particular, we establish the equivalence between reversibility, stable reversibility, and stable injectivity for ANUCA. We also prove the invertibility of several classes of injective and stably injective ANUCA. Counter-examples are given to highlight the differences between cellular automata and ANUCA.