On a series of finite automata defining free transformation groups

By Mariya Vorobets, Yaroslav Vorobets. 2006

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We introduce two series of finite automata starting from the so-called Aleshin and Bellaterra automata. We prove that transformations defined by automata from the first series generate a free non-Abelian group of infinite rank, while automata from the second series give rise to the free product of infinitely many groups of order 2.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5977313e1af13ba08e618cdfa7fd1f3d388e81c5