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 language | English |
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Pages (from-to) | 43-64 |
Number of pages | 22 |
Journal | Geometriae Dedicata |
Volume | 111 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2005 |
Keywords
- Commensurator
- Finite automata
- Free groups
- Property (T)
- Square complexes