Related papers: Automaticity of one-relator semigroups with length…
This paper shows how to construct explicitly an automaton that generates an arbitrary numerical semigroup.
A right [left] locally testable language S is a language with the property that for some non negative integer k two words u and v in alphabet S are equal in the semi group if (1) the prefix and suffix of the words of length k coincide, (2)…
This work introduces a new kind of affine semigroups called $P$-semigroups. Within the framework of $\mathcal C$-semigroups, we define a finite-state automaton associated to them. Moreover, this automaton determines whether a $\mathcal…
We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy…
We extend the two-variable logic on data words with guarded regular binary predicates of the form $\widetilde{L}(x,y)$ that is true if positions $x$ and $y$ are in the same class and the factor strictly between $x$ and $y$ is in the regular…
A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the…
We study congruences on the partial automorphism monoid of a finite rank free group action. We give a decomposition of a congruence on this monoid into a Rees congruence, a congruence on a Brandt semigroup and an idempotent separating…
In this paper we initiate the study of $\aleph_0$-categorical semigroups, where a countable semigroup $S$ is $\aleph_0$-categorical if, for any natural number $n$, the action of its group of automorphisms Aut $S$ on $S^n$ has only finitely…
We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we demonstrate a context-free…
Since first introduced by John von Neumann, the notion of cellular automaton has grown into a key concept in computer science, physics and theoretical biology. In its classical setting, a cellular automaton is a transformation of the set of…
We study the class of groups generated by automata that act essentially freely on the boundary of a rooted tree. In the process we establish and discuss some general tools for determining if a group belongs to this class, and explore the…
A word in a free group is called ``potentially positive'' if it is automorphic to an element which is written with only positive exponents. We will develop automata to analyze properties of potentially positive words. We will use these to…
A one-relator group is a group $G_r$ that admits a presentation $\langle S \mid r \rangle$ with a single relation $r$. One-relator groups form a rich classically studied class of groups in Geometric Group Theory. If $r \in F(S)'$, the…
We propose a way of associating to each finitely generated monoid or semigroup a formal language, called its loop problem. In the case of a group, the loop problem is essentially the same as the word problem in the sense of combinatorial…
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 prove several results regarding decidability of the membership problem for certain submonoids in amalgamated free products and HNN extensions of groups. These general results are then applied to solve the prefix membership…
Here we characterize regular and completely regular ordered semigroups by their minimal bi-ideals. A minimal bi-ideal is expressed as a product of a minimal right ideal and a minimal left ideal. Furthermore, we show that every bi-ideal in a…
A semigroupoid is a set equipped with a partially defined associative operation. Given a semigroupoid \Lambda we construct a C*-algebra C*(\Lambda) from it. We then present two main examples of semigroupoids, namely the Markov semigroupoid…
It is easy to see that if $\cG$ is a non-abelian group of unitary matrices, then for no members $A$ and $B$ of $\cG$ can the rank of $AB-BA$ be one. We examine the consequences of the assumption that this rank is at most two for a general…
After reviewing automaton semigroups, we introduce Cayley Automata and the corresponding Cayley Automaton semigroups. We investigate which semigroups are isomorphic to their Cayley Automaton semigroup and give some results for special…