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We construct automata over a binary alphabet with $2n$ states, $n\geq 2$, whose states freely generate a free group of rank $2n$. Combined with previous work, this shows that a free group of every finite rank can be generated by finite…
Eilenberg correspondence, based on the concept of syntactic monoids, relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence related more general classes of regular…
We describe a novel algorithm for random sampling of freely reduced words equal to the identity in a finitely presented group. The algorithm is based on Metropolis Monte Carlo sampling. The algorithm samples from a stretched Boltzmann…
Holt and R\"over proved that finitely generated bounded automata groups have indexed co-word problem. Here we sharpen this result to show they are in fact co-ET0L.
This paper grew out of three tutorial lectures on automatic structures given by the first author at the Logic Colloquium 2007. We discuss variants of automatic structures related to several models of computation: word automata, tree…
Stochastic automata are a formal compositional model for concurrent stochastic timed systems, with general distributions and non-deterministic choices. Measures of interest are defined over schedulers that resolve the nondeterminism. In…
In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…
Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of…
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 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…
We generalize the notion of a graph automatic group introduced by Kharlampovich, Khoussainov and Miasnikov (arXiv:1107.3645) by replacing the regular languages in their definition with more powerful language classes. For a fixed language…
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…
We consider $\omega^n$-automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length $\omega^n$ for some integer $n\geq 1$. We show that all these structures are…
We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new…
We explore a natural class of semigroups that have word problem decidable by finite state automata. Among the main results are invariance of this property under change of generators, invariance under basic algebraic constructions and…
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…
We consider decidability problems in self-similar semigroups, and in particular in semigroups of automatic transformations of $X^*$. We describe algorithms answering the word problem, and bound its complexity under some additional…
We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…
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…
We introduce session automata, an automata model to process data words, i.e., words over an infinite alphabet. Session automata support the notion of fresh data values, which are well suited for modeling protocols in which sessions using…