Automata and square complexes

Yair Glasner, Shahar Mozes

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reprove the theorem of Macedońska, Nekrashevych, Sushchansky, on the connection between bi-reversible automata and the commensurator of a regular tree.

Original languageEnglish
Pages (from-to)43-64
Number of pages22
JournalGeometriae Dedicata
Volume111
Issue number1
DOIs
StatePublished - 1 Mar 2005
Externally publishedYes

Keywords

  • Commensurator
  • Finite automata
  • Free groups
  • Property (T)
  • Square complexes

ASJC Scopus subject areas

  • Geometry and Topology

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