Related papers: Bounded Automata Groups are co-ET0L

We investigate the language classes recognized by group automata over matrix groups. For the case of $2 \times 2 $ matrices, we prove that the corresponding group automata for rational matrix groups are more powerful than the corresponding…

In this paper, we define the class of hourglass automata, which are timed automata with bounded clocks that can be made to progress backwards as well as forwards at a constant rate. We then introduce a new clock update for timed automata…

If $G$ is a finitely generated group and $X$ is a Cayley graph of $G$, denote by $\mathcal{C}_1^X(G)$ the subgroup of all automorphisms of $X$ commensurating $G$ and fixing the vertex corresponding to the identity. Building on the work of…

We show that there are Cayley automatic groups that are not Cayley biautomatic. In addition, we show that there are Cayley automatic groups with undecidable Conjugacy Problem and that the Isomorphism Problem is undecidable in the clas of…

We study automaton groups without singular points, that is, points in the boundary for which the map that associates to each point its stabilizer, is not continuous. This is motivated by the problem of finding examples of infinite…

In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to…

Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…

An approach to a classification of groups generated by 3-state automata over a 2-letter alphabet and the current progress in this direction are presented. Several results related to the whole class are formulated. In particular, all finite,…

We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one…

This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is…

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

The axioms of iteration theories, or iteration categories, capture the equational properties of fixed point operations in several computationally significant categories. Iteration categories may be axiomatized by the Conway identities and…

This paper contains results related to synthesis and presentation of abstract automata by fragments of behaviour and investigates the structure of the classes of finite connected initial output-less automata specified by systems of defining…

We study groups of reversible cellular automata, or CA groups, on groups. More generally, we consider automorphism groups of subshifts of finite type on groups. It is known that word problems of CA groups on virtually nilpotent groups are…

We prove that finite index subgroups in S-arithmetic Chevalley groups are bounded.

We describe an algorithm that computes the index of a finitely generated subgroup in a finitely $L$-presented group provided that this index is finite. This algorithm shows that the subgroup membership problem for finite index subgroups in…

The growth of a finitely generated group is an important geometric invariant which has been studied for decades. It can be either polynomial, for a well-understood class of groups, or exponential, for most groups studied by geometers, or…

We show that deterministic finite automata equipped with $k$ two-way heads are equivalent to deterministic machines with a single two-way input head and $k-1$ linearly bounded counters if the accepted language is strictly bounded, i.e., a…

This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers with the same input and output alphabet. The torsion problem…

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…