Abstract
Generalizing the idea of self-similar groups defined by Mealy automata, we introduce the notion of a self-similar automaton and a self-similar group over a changing alphabet. We show that every finitely generated residually-finite group is self-similar over an arbitrary unbounded changing alphabet. We construct some naturally defined self-similar automaton representations over an unbounded changing alphabet for any lamplighter group K{wreath product}Z with an arbitrary finitely generated (finite or infinite) abelian group K.
| Original language | English |
|---|---|
| Pages (from-to) | 96-110 |
| Number of pages | 15 |
| Journal | Theoretical Computer Science |
| Volume | 482 |
| DOIs | |
| Publication status | Published - 22 Apr 2013 |
Keywords
- Changing alphabet
- Group generated by an automaton
- Lamplighter group
- Rooted tree
- Time-varying automaton
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science
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