A note on cellular automata

2019/01/29 by M. Shahryari, Shahryari, M.
Computer Science · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1901.10160

openalex publication_date 2019/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

For an arbitrary group G and arbitrary set A, we define a monoid structure on the set of all uniformly continuous functions A^G→ A and then we show that it is naturally isomorphic to the monoid of cellular automata CA(G, A). This gives a new equivalent definition of a cellular automaton over the group G with alphabet set A. We use this new interpretation to give a simple proof of the theorem of Curtis-Hedlund.

Related

• Cellular automata on a G-set
• Von Neumann Regular Cellular Automata
• On Cellular Automata
• Further results on generalized cellular automata
• Universal groups of cellular automata