Automata and square complexes

Yair Glasner*, Shahar Mozes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


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 languageAmerican English
Pages (from-to)43-64
Number of pages22
JournalGeometriae Dedicata
Issue number1
StatePublished - Mar 2005


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


Dive into the research topics of 'Automata and square complexes'. Together they form a unique fingerprint.

Cite this