3,556 research outputs found
Integrated Structure and Semantics for Reo Connectors and Petri Nets
In this paper, we present an integrated structural and behavioral model of
Reo connectors and Petri nets, allowing a direct comparison of the two
concurrency models. For this purpose, we introduce a notion of connectors which
consist of a number of interconnected, user-defined primitives with fixed
behavior. While the structure of connectors resembles hypergraphs, their
semantics is given in terms of so-called port automata. We define both models
in a categorical setting where composition operations can be elegantly defined
and integrated. Specifically, we formalize structural gluings of connectors as
pushouts, and joins of port automata as pullbacks. We then define a semantical
functor from the connector to the port automata category which preserves this
composition. We further show how to encode Reo connectors and Petri nets into
this model and indicate applications to dynamic reconfigurations modeled using
double pushout graph transformation
Formal Relationships Between Geometrical and Classical Models for Concurrency
A wide variety of models for concurrent programs has been proposed during the
past decades, each one focusing on various aspects of computations: trace
equivalence, causality between events, conflicts and schedules due to resource
accesses, etc. More recently, models with a geometrical flavor have been
introduced, based on the notion of cubical set. These models are very rich and
expressive since they can represent commutation between any bunch of events,
thus generalizing the principle of true concurrency. While they seem to be very
promising - because they make possible the use of techniques from algebraic
topology in order to study concurrent computations - they have not yet been
precisely related to the previous models, and the purpose of this paper is to
fill this gap. In particular, we describe an adjunction between Petri nets and
cubical sets which extends the previously known adjunction between Petri nets
and asynchronous transition systems by Nielsen and Winskel
Higher-Dimensional Timed Automata
We introduce a new formalism of higher-dimensional timed automata, based on
van Glabbeek's higher-dimensional automata and Alur's timed automata. We prove
that their reachability is PSPACE-complete and can be decided using zone-based
algorithms. We also show how to use tensor products to combat state-space
explosion and how to extend the setting to higher-dimensional hybrid automata
History-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps
We show that history-preserving bisimilarity for higher-dimensional automata
has a simple characterization directly in terms of higher-dimensional
transitions. This implies that it is decidable for finite higher-dimensional
automata. To arrive at our characterization, we apply the open-maps framework
of Joyal, Nielsen and Winskel in the category of unfoldings of precubical sets.Comment: Minor updates in accordance with reviewer comments. Submitted to MFPS
201
A Fuzzy Petri Nets Model for Computing With Words
Motivated by Zadeh's paradigm of computing with words rather than numbers,
several formal models of computing with words have recently been proposed.
These models are based on automata and thus are not well-suited for concurrent
computing. In this paper, we incorporate the well-known model of concurrent
computing, Petri nets, together with fuzzy set theory and thereby establish a
concurrency model of computing with words--fuzzy Petri nets for computing with
words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of
transitions are some special words modeled by fuzzy sets. By employing the
methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which
makes it possible for computing with more words. The language expressiveness of
the two formal models of computing with words, fuzzy automata for computing
with words and FPNCWs, is compared as well. A few small examples are provided
to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure
A regular viewpoint on processes and algebra
While different algebraic structures have been proposed for the treatment of concurrency, finding solutions for equations over these structures needs to be worked on further. This article is a survey of process algebra from a very narrow viewpoint, that of finite automata and regular languages. What have automata theorists learnt from process algebra about finite state concurrency? The title is stolen from [31]. There is a recent survey article [7] on finite state processes which deals extensively with rational expressions. The aim of the present article is different. How do standard notions such as Petri nets, Mazurkiewicz trace languages and Zielonka automata fare in the world of process algebra? This article has no original results, and the attempt is to raise questions rather than answer them
Higher Dimensional Transition Systems
We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures
Generalized Asynchronous Systems
The paper is devoted to a mathematical model of concurrency the special case
of which is asynchronous system. Distributed asynchronous automata are
introduced here. It is proved that the Petri nets and transition systems with
independence can be considered like the distributed asynchronous automata. Time
distributed asynchronous automata are defined in standard way by the map which
assigns time intervals to events. It is proved that the time distributed
asynchronous automata are generalized the time Petri nets and asynchronous
systems.Comment: 8 page
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