Related papers: On the ET0L subgroup membership problem in bounded…
A classical result of Schreier states that nontrivial finitely generated normal subgroups of free groups are of finite index, that is, free groups can only quotient to finite groups with finitely generated kernel. In this note we extend…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constructible EDT0L language. In particular, the set of all solutions in reduced words is an indexed…
We investigate the computational power of periodically iterated morphisms, also known as D0L systems with periodic control, PD0L systems for short. These systems give rise to a class of one-sided infinite sequences, called PD0L words. We…
We present obstruction results for self-similar groups regarding the generation of free groups. As a main consequence of our main results, we solve an open problem posed by Grigorchuk by showing that in an automaton group where 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…
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…
We revisit the membership problem for subclasses of rational relations over finite and infinite words: Given a relation R in a class C_2, does R belong to a smaller class C_1? The subclasses of rational relations that we consider are formed…
In this article, we study the fixed-point subgroups of the solvable Baumslag-Solitar groups $\BS(1,n)= \langle a, t \mid t a t^{-1} = a^{n} \rangle$, $n>1$ of automorphisms and endomorphisms. We also investigate the stabilizers of subgroups…
A finitely generated group is said to be an automata group if it admits a faithful self-similar finite-state representation on some regular $m$-tree. We prove that if $G$ is a subgroup of an automata group, then for each finitely generated…
We study the dynamic membership problem for regular tree languages under relabeling updates: we fix an alphabet $\Sigma$ and a regular tree language $L$ over $\Sigma$ (expressed, e.g., as a tree automaton), we are given a tree $T$ with…
We give a simple algorithm to solve the subgroup membership problem for virtually free groups. For a fixed virtually free group with a fixed generating set $X$, the subgroup membership problem is uniformly solvable in time $O(n\log^*(n))$…
We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as…
We introduce the notion of a subgraph generated by an $R$-word $r$ of the Sch\"{u}tzenberger graph of a positive word $w$, $S\Gamma(w)$, where $w$ contains $r$ as its subword. We show that the word problem for a finitely presented Adian…
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…
This work is a contribution to the study of set of the representations of integers in a rational base number system. This prefix-closed subset of the free monoid is naturally represented as a highly non regular tree whose nodes are the…
The category of all idempotent generated semigroups with a prescribed structure $\mathcal{E}$ of their idempotents $E$ (called the biordered set) has an initial object called the free idempotent generated semigroup over $\mathcal{E}$,…
We study automaton structures, i.e. groups, monoids and semigroups generated by an automaton, which, in this context, means a deterministic finite-state letter-to-letter transducer. Instead of considering only complete automata, we…
We show that the following problems are decidable in a rank 2 free group F_2: does a given finitely generated subgroup H contain primitive elements? and does H meet the orbit of a given word u under the action of G, the group of…
Motivated by approaches to the word problem for one-relation monoids arising from work of Adian and Oganesian (1987), Guba (1997), and Ivanov, Margolis and Meakin (2001), we study the submonoid and rational subset membership problems in…