Archivo de la etiqueta: coalgebra

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

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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

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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.

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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.

Visita Jan Rutten

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Mar ’13Mar
1115

Foto Jan RuttenEl profesor Jan Rutten visitará el Departament d’Àlgebra de la Universitat de València entre el 11 y el 15 de marzo de 2013. Jan Rutten es investigador sénior del CWI (Centro de Matemáticas e Informática), Ámsterdam, y profesor de informática teórica en la Universidad de Radboud, Nijmegen. Ha sido uno de los fundadores de la coálgebra universal, que es una teoría general del comportamiento circular de autómatas, sistemas dinámicos y estructuras de datos infinitos. Ha sido uno de los iniciadores de la serie de encuentros «Coalgebraic Methods in Computer Science» (CMCSC) y la «Conference on Algebra and Coalgebra in Computer Science (CALCO). Sus intereses en investigación incluyen los fundamentos coalgebraicos de la computación y los métodos formales para la ingeniería de la programación, especialmente programación orientada a servicios y basada en componentes.

 

Charla Jan Rutten

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Mar ’13
13
11:00

El profesor Jan Rutten, CWI, Ámsterdam, y Universidad Radboud, Nijmegen, que nos visita entre el 11 y el 15 de marzo, impartirá la charla titulada

The method of coalgebra – an overview

el próximo miércoles 13 de marzo de 2013, a las 11.00, en el seminario del Departament d’Àlgebra de la Universitat de València (Facultat de Matemàtiques, 2º piso).

Resumen:

Since the early nineties, coalgebra has become an active area of research in which one tries to understand all kinds of infinite data types, automata, transition systems and dynamical systems from a unifying perspective. The focus of coalgebra is on observable behaviour and one uses coinduction as a central methodology, both for behavioural specifications and to prove behavioural equivalences. These days, one uses coalgebraic techniques in a wide variety of areas, ranging from automata theory to software engineering to ecology. In this talk, we shall illustrate the coalgebraic approach by discussing a number examples, including streams, automata and circuits.

Estáis todos invitados.