Polynomial Synthesis of Asynchronous Automata

Zielonka's theorem shows that each regular set of Mazurkiewicz traces can be implemented as a system of synchronized processes with a distributed control structure called asynchronous automaton. This paper gives a polynomial algorithm for the synthesis of a non-deterministic asynchronous automaton from a regular Mazurkiewicz trace language. This new construction is based on an unfolding approach that improves the complexity of Zielonka's and Pighizzini's techniques in terms of the number of states.Comment: The MOdelling and VErification (MOVE) tea

CONSTRUCTION OF ASYMMETRIC CHUDNOVSKY ALGORITHMS WITHOUT DERIVATED EVALUATION FOR MULTIPLICATION IN FINITE FIELDS

The Chudnovsky and Chudnovsky algorithm for the multiplication in extensions of finite fields provides a bilinear complexity which is uniformly linear with respect to the degree of the extension. Recently, Ran-driambololona has generalized the method, allowing asymmetry in the interpolation procedure and leading to new upper bounds on the bilinear complexity. In this article, we first translate this generalization into the language of algebraic function fields. Then, we propose a strategy to effectively construct asymmetric algorithms using places of higher degrees and without derivated evaluation. Finally, we provide examples of three multiplication algorithms along with their Magma implementation: in F 16 13 using only rational places, in F 4 5 using also places of degree two, and in F 2 5 using also places of degree four

Weighted Automata and Expressions over Pre-Rational Monoids

The Kleene theorem establishes a fundamental link between automata and expressions over the free monoid. Numerous generalisations of this result exist in the literature; on one hand, lifting this result to a weighted setting has been widely studied. On the other hand, beyond the free monoid, different monoids can be considered: for instance, two-way automata, and even tree-walking automata, can be described by expressions using the free inverse monoid. In the present work, we aim at combining both research directions and consider weighted extensions of automata and expressions over a class of monoids that we call pre-rational, generalising both the free inverse monoid and graded monoids. The presence of idempotent elements in these pre-rational monoids leads in the weighted setting to consider infinite sums. To handle such sums, we will have to restrict ourselves to rationally additive semirings. Our main result is thus a generalisation of the Kleene theorem for pre-rational monoids and rationally additive semirings. As a corollary, we obtain a class of expressions equivalent to weighted two-way automata, as well as one for tree-walking automata

The Pros and Cons of Netcharts

Abstract. Netcharts have been introduced recently by Mukund et al. in [17]. This new appealing approach to the specification of collections of message sequence charts (MSCs) benefits from a graphical description, a formal semantics based on Petri nets, and an appropriate expressive power. As opposed to high-level MSCs, any regular MSC language is the language of some netchart. Motivated by two open problems raised in [17], we establish in this paper that the questions (i) whether a given high-level MSC describes some netchart language (ii) whether a given netchart is equivalent to some high-level MSC (iii) whether a given netchart describes a regular MSC language are undecidable. These facts are closely related to our first positive result: We prove that netchart languages are exactly the MSC languages that are implementable by message passing automata up to refinement of message contents. Next we focus on FIFO netcharts: The latter are defined as the netcharts whose executions correspond to all firing sequences of their low-level Petri net. We show that the questions (i) whether a netchart is a FIFO netchart (ii) whether a FIFO netchart describes a regular MSC language (iii) whether a regular netchart is equivalent to some high-level MSC are decidable

Synthèse d'automates asynchrones et communicants

Les automates asynchrones constituent un modèle qui décrit explicitement le parallélisme des exécutions dans un système distribué à mémoires partagées. Au contraire, les id-automates décrivent l'ensemble des exécutions séquentielles du comportement d'un tel système. Nous avons élaboré une technique de dépliage inédite qui construit à partir d'un id-automate à un automate asynchrone sémantiquement équivalent à A de taille polynomiale à A. Cette construction améliore les complexités des constructions existantes. Les automates communicants (CFM) modélisent des systèmes distribués à passages de messages. Les protocoles de communication employés dans de tels systèmes peuvent être spécifiés au moyen de diagrammes de communication (MSCS). Nous caractérisons les ensembles de MSCS qui peuvent être implémentés en un CFM sans blocage et avec arrêt définitif. Enfin, nous explorons le formalisme des netcharts. Nous montrons entre autres que les modèles des netcharts et des CFMS sont équivalents.AIX-MARSEILLE1-BU Sci.St Charles (130552104) / SudocSudocFranceF