Related papers: Examples of defining groups by finite automata

Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this…

We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not…

Every self-similar group acts on the space $X^\omega$ of infinite words over some alphabet $X$. We study the Schreier graphs $\Gamma_w$ for $w\in X^\omega$ of the action of self-similar groups generated by bounded automata on the space…

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2^n states, where n is the maximal length of words…

Let $\psi$ be a permutation of a finite set $X$. We define $\lambda(\psi)$ to be the largest fraction of elements of $X$ lying on a single cycle of $\psi$. For a finite group $G$, we define $\lambda(G)$ to be the maximum among the values…

This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of…

This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating…

Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but…

In this paper, we introduce the notion of strongly automatic semigroup, which implies the usual notion of auto- maticity. We focus on semigroups of \beta-adics developpements, for which we obtain a criterion of strong automaticity.

We find a set of generators for the automorphism group of a graph product of finitely generated abelian groups entirely from a certain labeled graph. In addition, we find generators for the important subgroup of star-automorphisms defined…

Let $G$ be a finite group and $\alpha(G)=\frac{|C(G)|}{|G|}$\,, where $C(G)$ denotes the set of cyclic subgroups of $G$. In this short note, we prove that $\alpha(G)\leq\alpha(Z(G))$ and we describe the groups $G$ for which the equality…

We provide an algorithm to solve the word problem in all fundamental groups of closed 3-manifolds; in particular, we show that these groups are autostackable. This provides a common framework for a solution to the word problem in any closed…

Let $F$ be a finite field of characteristic $p$. The structures of the unit groups of group algebras over $F$ of the three groups $D_{24}$, $S_4$ and $SL(2, \mathbb{Z}_3)$ of order $24$ are completely described in \cite{K4, SM, SM1, FM,…

For an arbitrary countable group G = <A|R> given by its generators A and defining relations R we discuss a specific method for embedding of G into a certain 2-generator group T. Our embedding explicitly lists the images of generators from A…

Bruyere and Carton lifted the notion of finite automata reading infinite words to finite automata reading words with shape an arbitrary linear order L. Automata on finite words can be used to represent infinite structures, the so-called…

In this note, we consider models in $\mathbb C^2$. The purpose of this note is twofold. We first show a characterization of models in $\mathbb C^2$ by their noncompact automorphism groups. Then we give an explicit description for…

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

We consider the class of finitely generated groups whose relators are powers of commutators of the generators. This class contains as a small subclass graph groups (also called RAAGs), namely if all powers are one. Graph groups are the only…

We investigate the relationship between finite groups and incidence geometries through their automorphism structures. Building upon classical results on the realizability of groups as automorphism groups of graphs, we develop a general…

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…