Search results for " 68Q70"
showing 6 items of 6 documents
Machine $B_4$
2020
We construct map $\xi$. It exhibits dense orbits for all $x\in\overline{0,1}^\omega$. We give elementary proofs for all statements.
The infinite dihedral group
2022
We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.
Languages associated with saturated formations of groups
2013
International audience; In a previous paper, the authors have shown that Eilenberg's variety theorem can be extended to more general structures, called formations. In this paper, we give a general method to describe the languages corresponding to saturated formations of groups, which are widely studied in group theory. We recover in this way a number of known results about the languages corresponding to the classes of nilpotent groups, soluble groups and supersoluble groups. Our method also applies to new examples, like the class of groups having a Sylow tower.; Dans un article précédent, les auteurs avaient montré comment étendre le théorème des variétés d'Eilenberg à des structures plus g…
Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited
2014
International audience; We present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.; Nous présentons une extension du théorème des variétés d'Eilenberg, un résultat célèbre reliant l'algèbre à la théorie des langages formels. Nous montrons qu'il existe une correspondance bijective entre les form…
Automaton (Semi)groups (Basic Concepts)
2018
In this paper, we give an introduction to basic concepts of automaton semigroups. While we must note that this paper does not contain new results, it is focused on extended introduction in the subject and detailed examples.
Varieties Generated by Certain Models of Reversible Finite Automata
2006
Reversible finite automata with halting states (RFA) were first considered by Ambainis and Freivalds to facilitate the research of Kondacs-Watrous quantum finite automata. In this paper we consider some of the algebraic properties of RFA, namely the varieties these automata generate. Consequently, we obtain a characterization of the boolean closure of the classes of languages recognized by these models.