On (bi)reversible automata generating lamplighter groups

2023/08/10 by Piotr W. Nowak, Nowak, Piotr W., Andriy Oliynyk +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #20E08 (Primary) #20E22 #20E26 (Secondary) #Cellular Automata and Applications #DNA and Biological Computing #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2308.05808

openalex publication_date 2023/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any nontrivial abelian group \mathbbX we construct a reversible (bireversible in case the order of \mathbbX is odd) automaton such that its set of states and alphabet are identified with \mathbbX, transition and output functions are defined via the left and the right regular actions correspondingly and its group splits into the restricted wreath product \mathbbX \wr ℤ, i.e. is a lamplighter group.

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