Actualització: Defensa tesi doctoral Enric Cosme 22/10/2015, 12.00, sala graus Química

Oct ’15
22
12:00

portadaTesiEnricCosmeEl proper dijous 22 d’octubre de 2015, a les 12.00, a la sala de graus de la Facultat de Química de la Universitat de València (carrer de Vicent Andrés Estellés, s/n, Burjassot), es procedirà a la defensa de la tesi doctoral d’Enric Cosme i Llópez, dirigida per Adolfo Ballester Bolinches i Jean-Éric Pin i amb títol

«Some contributions to the algebraic theory of automata».

Esteu convidats a assistir a aquest acte.

 Actualització 16/10/2015: La defensa es durà a terme a la sala de graus de la Facultat de Química i no a la de Farmàcia, com inicialment estava previst.

Paper “A description based on languages of the final non-deterministic automaton” published in Theoret. Comput. Sci.

The following paper has been published:

El siguiente artículo ha sido publicado:

El següent article ha sigut publicat:

A. Ballester-Bolinches, E. Cosme-Llópez, R. Esteban-Romero

A description based on languages of the final non-deterministic automaton

Theoret. Comput. Sci., 536 (2014), 1–20

http://dx.doi.org/10.1016/j.tcs.2014.01.018

Abstract

The study of the behaviour of non-deterministic automata has traditionally focused on the languages which can be associated to the different states. Under this interpretation, the different branches that can be taken at every step are ignored. However, we can also take into account the different decisions which can be made at every state, that is, the branches that can be taken, and these decisions might change the possible future behaviour. In this case, the behaviour of the automata can be described with the help of the concept of bisimilarity. This is the kind of description that is usually obtained when the automata are regarded as labelled transition systems or coalgebras.

Contrarily to what happens with deterministic automata, it is not possible to describe the behaviour up to bisimilarity of states of a non-deterministic automaton by considering just the languages associated to them. In this paper we present a description of a final object for the category of non-deterministic automata, regarded as labelled transition systems, with the help of some structures defined in terms of languages. As a consequence, we obtain a characterisation of bisimilarity of states of automata in terms of languages and a method to minimise non-deterministic automata with respect to bisimilarity of states. This confirms that languages can be considered as the natural objects to describe the behaviour of automata.

Keywords: Non-deterministic automaton; Formal language; Coalgebra; Bisimilarity; Final automaton

Paper “A description based on languages of the final non-deterministic automaton” accepted in Theoretical Computer Science

The paper “A description based on languages of the final non-deterministic automaton” has been accepted for publication in Theoretical Computer Science. The abstract can be found below. We will inform later about the publication details. It will be available on

http://dx.doi.org/10.1016/j.tcs.2014.01.018.

El artículo “A description based on languages of the final non-deterministic automaton” ha sido aceptado para su publicación en Theoretical Computer Science. El resumen aparece más abajo. Informaremos más adelante sobre los detalles bibliográficos. Estará disponible en

http://dx.doi.org/10.1016/j.tcs.2014.01.018.

L’article “A description based on languages of the final non-deterministic automaton” ha sigut acceptat per a la seua publicació en Theoretical Computer Science. El resum apareix davall. Informarem més endavant sobre els detalls bibliogràfics. Estarà disponible en

http://dx.doi.org/10.1016/j.tcs.2014.01.018.

Abstract: The study of the behaviour of non-deterministic automata has traditionally focused on the languages which can be associated to the different states. Under this interpretation, the different branches that can be taken at every step are ignored. However, we can also take into account the different decisions which can be made at every state, that is, the branches that can be taken, and these decisions might change the possible future behaviour. In this case, the behaviour of the automata can be described with the help of the concept of bisimilarity. This is the kind of description that is usually obtained when the automata are regarded as labelled transition systems or coalgebras.

Contrarily to what happens with deterministic automata, it is not possible to describe the behaviour up to bisimilarity of states of a non-deterministic automaton by considering just the languages associated to them. In this paper we present a description of a final object for the category of non-deterministic automata, regarded as labelled transition systems, with the help of some structures defined in terms of languages. As a consequence, we obtain a characterisation of bisimilarity of states of automata in terms of languages and a method to minimise non-deterministic automata with respect to bisimilarity of states. This
confirms that languages can be considered as the natural objects to describe the behaviour of automata.

Mathematics Subject Classification (2010): 68Q70, 68Q45, 68Q55, 18B20
Keywords: non-deterministic automaton, formal language, coalgebra, bisimilarity, final automaton.

Paper “Varieties and covarieties of languages (extended abstract)” published in Electron. Notes Theor. Comput. Sci.

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

Jan Rutten, Adolfo Ballester-Bolinches, Enric Cosme-Llópez

Varieties and covarieties of languages (extended abstract)

Electron. Notes Theor. Comput. Sci., 298, 7-28 (2013)

http://dx.doi.org/10.1016/j.entcs.2013.09.005

Abstract: Because of the isomorphism (X × A) → X =∼ X → (A → X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebra-coalgebra duality goes back to Arbib and Manes, who formulated it as a duality between reachability and observability, and is ultimately based on Kalman’s duality in systems theory between controllability and observability. Recently, it was used to give a new proof of Brzozowski’s minimization algorithm for deterministic automata. Here we will use the algebra-coalgebra duality of automata as a common perspective for the study of both varieties and covarieties, which are classes of automata and languages defined by equations and coequations, respectively. We make a first connection with Eilenberg’s definition of varieties of languages, which is based on the classical, algebraic notion of varieties of (transition) monoids.
Keywords:
Automata, variety, covariety, equation, coequation, algebra, coalgebra.

Paper “Algorithms for permutability in finite groups” published in Cent. Eur. J. Math.

The following paper has been published:

El siguiente artículo ha sido publicado:

El següent article ha sigut publicat:

A. Ballester-Bolinches, E. Cosme-Llópez, R. Esteban-Romero

Algorithms for permutability in finite groups

Cent. Eur. J. Math., 11 (11), 1914-1922 (2013).

Abstract: In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.

Keywords:  Finite group • Permutable subgroup • S-permutable subgroup • Dedekind group • Iwasawa group • T-group • PT-group • PST-group • Algorithm
Mathematics Subject Classification (2010):  20D10, 20D20, 20-04

http://dx.doi.org/10.2478/s11533-013-0299-4