In the two-sided pushdown automata discussed in this paper, their two-sided pushdowns are introduced over free groups rather than free monoids. It is demonstrated that these automata with pushdowns introduced in this way characterize the family of recursively enumerable languages.

Let V be a finite-dimensional vector space over a field K and let G be a sofic group. We show that every injective linear cellular automaton τ : V G → V G is surjective. As an application, we obtain a new proof of the stable finiteness of group rings of sofic groups, a result previously established by G. Elek and A. Szabó using different methods.

We prove that the boundary dynamics of the (semi)group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group. We specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to have a finite Schreier graph in the boundary of the enriched dual pointed on some essentially...

Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

We explore the connections between automata, groups, limit spaces of self-similar actions, and tilings. In particular, we show how a group acting “nicely” on a tree gives rise to a self-covering of a topological groupoid, and how the group can be reconstructed from the groupoid and its covering. The connection is via finite-state automata. These define decomposition rules, or self-similar tilin...

In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups " expanding automaton semigroups ". W...

We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is π-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the local functions permute the periodic points, and these permutations generate the dynamics group. We have previously shown that exactly 104 of the possible 22 3...