Thèse de doctorat : Automatique, Traitement du Signal, Génie Informatique : Nancy 1 : 2007. / Titre provenant de l'écran-titre. Bibliogr.

Thesis (M.Eng.)--Memorial University of Newfoundland, 2000. / Bibliography: leaves 74-79.

Thesis--M. Phil., University of Hong Kong, 1986.

published_or_final_version / Computer Science / Master / Master of Philosophy

Η εργασία ασχολείται με τα Ασαφή Δίκτυα Petri. Αφού γίνει μιά ιστορική αναδρομή στα Δίκτυα Petri, στη συνέχεια αναπτύσονται τα διάφορα είδη δικτύων Petri καθώς επίσης και οι ιδιότητές τους. Επιπλέον, αναλύονται κάποιες βασικές έννοιες σχετικά με τις υπολειμματικές δομές, τα ασαφή σύνολα, την ασαφή λογική, τις ομάδες δικτυωτής διάταξης και τις MV-Άλγεβρες. Αυτές οι έννοιες είναι απαραίτητες για τα Ασαφή Δίκτυα Petri και κυρίως για την ανάπτυξη της λεγόμενης Petri Άλγεβρας. Τέλος αναλύονται κάποιες εφαρμογές των Ασαφών Δικτύων Petri. / This project is about Fuzzy Petri Nets. After a historical introduction in Petri Nets, we analyze the different types of Petri Nets as well as their properties. Furthermore, we focus on some basic concepts of the residuated structures, fuzzy sets, fuzzy logic, lattice-ordered abelian groups and MV-Algebras. These concepts are essential for Fuzzy Petri Nets and Petri Algebras. Finally, we analyze some basic applications of Fuzzy Petri Nets.

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El objetivo de la tesis es la definición de un modelo de ejecución paralelo, que basado en la representación de un algoritmo paralelo con Redes de Petri, permita a un conjunto flexible de procesadores independientes entre sí, ejecutar el algoritmo en forma asíncrona con altos rendimientos y que el programador tenga capacidad de ajustar los parámetros de ejecución en vista de mejoras de rendimiento. Los fundamentos son claros: se desea contar con una herramienta de ejecución de programas paralelos que permita modelar el algoritmo, y pasar del modelo a la ejecución asíncrona preservando el modelo. Las Redes de Petri son la herramienta básica e indiscutiblemente pertinente para lograr el objetivo. Un desafío es cubrir la brecha o gap existente entre el modelado y una ejecución del programa paralelo de rendimientos aceptables y escalables.Para ello, debe existir una vinculación del modelo con un conjunto de unidades de procesamiento que corran en paralelo.

Petri nets are used as models in the study of networks involving information flows. Petri nets have also turned out to be useful in the study of many asynchronous concurrent systems.In this thesis, the notions of deadlocks, traps, and liveness are considered from a graph theoretic viewpointA characterization of minimal deadlocks and traps in Petri nets is obtained. For the complete Petri nets, alternative characterizations of deadlocks and traps are obtained. Necessary and sufficient conditions are obtained for complete Petri nets to be deadlock free. Similar conditions for trap free complete Petri nets are also determined. / Department of Computer Science

The Petri Box Calculus (PBC) consists of an algebra of box expressions, and a corresponding algebra of boxes (a class of labelled Petri nets). A compo- sitional semantics provides a translation from box expressions to boxes. The synthesis problem is to provide an algorithmic translation from boxes to box expressions. The axiomatisation problem is to provide a sound and complete axiomatisation for the fragment of the calculus under consideration, which captures a particular notion of equivalence for boxes. There are several alternative ways of defining an equivalence notion for boxes, the strongest one being net isomorphism. In this thesis, the synthesis and axiomatisation problems are investigated for net semantic isomorphism, and a slightly weaker notion of equivalence, called duplication equivalence, which can still be argued to capture a very close structural similarity of con- current systems the boxes are supposed to represent. In this thesis, a structured approach to developing a synthesis algorithm is proposed, and it is shown how this may be used to provide a framework for the production of a sound and complete axiomatisation. This method is used for several different fragments of the Petri Box Calculus, and for gener- ating axiomatisations for both isomorphism and duplication equivalence. In addition, the algorithmic problems of checking equivalence of boxes and box expressions, and generating proofs of equivalence are considered as extensions to the synthesis algorithm.