In this paper, we study algorithmic problems for automaton semigroups and automaton groups related to freeness and finiteness. In the course of this study, we also exhibit some connections between the algebraic structure of automaton (semi)groups and their dynamics on the boundary. First, we show that it is undecidable to check whether the group generated by a given invertible automaton has a p...

This paper gives decidable conditions for when a nitely generated subgroup of a free group is the fundamental group of a Sch utzenberger automaton corresponding to a monoid presentation of an inverse monoid. Also, generalizations are given to speciic types of inverse monoids as well as to monoids which are \nearly inverse." This result has applications to computing membership for inverse monoid...

he purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and ...

Given a shift subspace over a finitely generated group, we define the subshift induced by it on a larger group. Then we do the same with cellular automata and, while observing that the new automaton can model a different abstract dynamics, we remark several properties that are shared with the old one. After that, we simulate the old automaton inside the new one, and discuss some consequences an...

We apply the dinamically driven renormalization group to study the critical properties of the Domany-Kinzel probabilistic cellular automaton. To preserve the absorbing state clusters with at least one site occupied are renormalized into a one occupied site and clusters with all sites empty are renormalized into a one empty site. We have obtained the phase diagram as well as the critical exponen...

We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group