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arXiv · 1702.00435

On groups generated by bi-reversible automata: the two-state case over a changing alphabet

Adam Woryna
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Abstract

The notion of an automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ is used to define and study automorphism groups of the tree $X^*$ of finite words over $X$. The concept of bi-reversibility for Mealy-type automata is extended to automata over a changing alphabet. It is proved that a non-abelian free group can be generated by a two-state bi-reversible automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ if and only if $X$ is unbounded. The characterization of groups generated by a two-state bi-reversible automaton over the sequence of binary alphabets is established.

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Adam Woryna. 2017-02-01. On groups generated by bi-reversible automata: the two-state case over a changing alphabet. https://doi.org/10.1016/j.jcss.2017.01.004

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