Related papers: Groups generated by 3-state automata over a 2-lett…

Generalizing the idea of self-similar groups defined by Mealy automata, we itroduce the notion of a self-similar automaton and a self-similar group over a changing alphabet. We show that every finitely generated residually-finite group is…

We are following [4]. Nevertheless we are interested only in claryfication that the lamplighter group can be realized as a 2--states Mealy machine.

We describe the development of the theory of automatic groups. We begin with a historical introduction, define the concepts of automatic, biautomatic and combable groups, derive basic properties, then explain how hyperbolic groups and the…

Automorphism groups of $2$-groups of coclass at most $3$ are investigated.

In this paper, we continue the classification work done in the first paper of the same name. With careful modifications of our previous approach, we are able to deduce (with two notable exceptions) which members of the previously introduced…

We add to the classification of groups generated by 3-state automata over a 2 letter alphabet given by Bondarenko et al., by showing that a number of the groups in the classification are non-contracting. We show that the criterion we use to…

We prove several new results on the structure of the subgroup generated by a small doubling subset of an ordered group, abelian or not. We obtain precise results generalizing Freiman's 3k-3 and 3k-2 theorems in the integers and several…

We construct group codes over two letters (i.e., bases of subgroups of a two-generated free group) with special properties. Such group codes can be used for reducing algorithmic problems over large alphabets to algorithmic problems over a…

We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an…

This is a continuation of an earlier preprint (math.GT/0209121) under the same title. These papers grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or…

We investigate the language classes recognized by group automata over matrix groups. We present a summary of the results obtained so far together with a number of new results. We look at the computational power of time-bounded group…

We classify abelian subgroups of two-dimensional Artin groups.

In this paper we introduce the concept of a Cayley graph automatic group (CGA group or graph automatic group, for short) which generalizes the standard notion of an automatic group. Like the usual automatic groups graph automatic ones enjoy…

We study the action of groups generated by bounded activity automata with infinite alphabets on their orbital Schreier graphs. We introduce an amenability criterion for such groups based on the recurrence of the first level action. This…

We give a new computer-assisted proof of the classification of maximal subgroups of the simple group ${}^2E_6(2)$ and its extensions by any subgroup of the outer automorphism group $S_3$. This is not a new result, but no earlier proof…

This report assumes the basics of inverse semigroup theory as described in the first primer but goes on to show how they may be analysed using ideas from category theory.

This work delved into the realm of automatic text generation, exploring a variety of techniques ranging from traditional deterministic approaches to more modern stochastic methods. Through analysis of greedy search, beam search, top-k…

The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, there are some classes of automata that do not contain such examples. For instance, all infinite Burnside automaton groups in the…

In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…

We give a simpler proof using automata theory of a recent result of Kapovich, Weidmann and Myasnikov according to which so-called benign graphs of groups preserve decidability of the generalized word problem. These include graphs of groups…