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Automata and Square Complexes

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL, 60607-7045, U.S.A

    Yair Glasner

  2. Institute of Mathematics, The Hebrew University, Jerusalem, 91904, Israel

    Shahar Mozes

Authors
  1. Yair Glasner
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  2. Shahar Mozes
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Correspondence to Yair Glasner.

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Glasner, Y., Mozes, S. Automata and Square Complexes. Geom Dedicata 111, 43–64 (2005). https://doi.org/10.1007/s10711-004-1815-2

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