9,740 research outputs found
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
A Kleene theorem for Petri automata
While studying the equational theory of Kleene Allegories (KAl), we recently proposed two ways of defining sets of graphs [BP15]: from KAl expressions, that is, regular expressions with intersection and converse; and from a new automata model, Petri automata, based on safe Petri nets. To be able to compare the sets of graphs generated by KAl expressions, we explained how to construct Petri automata out of arbitrary KAl expressions. In the present paper, we describe a reverse transformation: recovering an expression from an automaton. This has several consequences. First, it generalises Kleene theorem: the graph languages specified by Petri automata are precisely the languages denoted by KAl expressions. Second, this entails that decidability of the equa-tional theory of Kleene Allegories is equivalent to that of language equivalence for Petri automata. Third, this transformation may be used to reason syntactically about the occurrence nets of a safe Petri net, provided they are parallel series
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
Reachability of Communicating Timed Processes
We study the reachability problem for communicating timed processes, both in
discrete and dense time. Our model comprises automata with local timing
constraints communicating over unbounded FIFO channels. Each automaton can only
access its set of local clocks; all clocks evolve at the same rate. Our main
contribution is a complete characterization of decidable and undecidable
communication topologies, for both discrete and dense time. We also obtain
complexity results, by showing that communicating timed processes are at least
as hard as Petri nets; in the discrete time, we also show equivalence with
Petri nets. Our results follow from mutual topology-preserving reductions
between timed automata and (untimed) counter automata.Comment: Extended versio
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
Compositions of (max, +) automata
This paper presents a compositional modeling approach by means of (max, +) automata. The motivation is to be able to model a complex discrete event system by composing sub-models representing its elementary parts. A direct modeling of safe timed Petri nets using (max, +) automata is first introduced. Based on this result, two types of synchronous product of (max, +) automata are proposed to model safe timed Petri nets obtained by merging places and/or transitions in subnets. An asynchronous product is finally proposed to represent particular bounded timed Petri nets
Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets
Two formal stochastic models are said to be bisimilar if their solutions as a
stochastic process are probabilistically equivalent. Bisimilarity between two
stochastic model formalisms means that the strengths of one stochastic model
formalism can be used by the other stochastic model formalism. The aim of this
paper is to explain bisimilarity relations between stochastic hybrid automata,
stochastic differential equations on hybrid space and stochastic hybrid Petri
nets. These bisimilarity relations make it possible to combine the formal
verification power of automata with the analysis power of stochastic
differential equations and the compositional specification power of Petri nets.
The relations and their combined strengths are illustrated for an air traffic
example.Comment: 15 pages, 4 figures, Workshop on Formal Methods for Aerospace (FMA),
EPTCS 20m 201
On detectability of labeled Petri nets and finite automata
We study detectability properties for labeled Petri nets and finite automata.
We first study weak approximate detectability (WAD) that implies that there
exists an infinite observed output sequence of the system such that each prefix
of the output sequence with length greater than a given value allows an
observer to determine if the current state belongs to a given set. We also
consider two new concepts called instant strong detectability (ISD) and
eventual strong detectability (ESD). The former property implies that for each
possible infinite observed output sequence each prefix of the output sequence
allows reconstructing the current state. The latter implies that for each
possible infinite observed output sequence, there exists a value such that each
prefix of the output sequence with length greater than that value allows
reconstructing the current state.
Results: WAD: undecidable for labeled Petri nets, PSPACE-complete for finite
automata ISD: decidable and EXPSPACE-hard for labeled Petri nets, belongs to P
for finite automata ESD: decidable under promptness assumption and
EXPSPACE-hard for labeled Petri nets, belongs to P for finite automata SD:
belongs to P for finite automata, strengthens Shu and Lin's 2011 results based
on two assumptions of deadlock-freeness and promptness ISD<SD<ESD<WD<WAD for
both labeled Petri nets and finite automataComment: 44 pages, 21 figure
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