1,709 research outputs found
Characterizing Behavioural Congruences for Petri Nets
We exploit a notion of interface for Petri nets in order to design a set of net combinators. For such a calculus of nets, we focus on the behavioural congruences arising from four simple notions of behaviour, viz., traces, maximal traces, step, and maximal step traces, and from the corresponding four notions of bisimulation, viz., weak and weak step bisimulation and their maximal versions. We characterize such congruences via universal contexts and via games, providing in such a way an understanding of their discerning powers
Homology and Bisimulation of Asynchronous Transition Systems and Petri Nets
Homology groups of labelled asynchronous transition systems and Petri nets
are introduced. Examples of computing the homology groups are given. It is
proved that if labelled asynchronous transition systems are bisimulation
equivalent, then they have isomorphic homology groups. A method of constructing
a Petri net with given homology groups is found.Comment: 21 page
Petri nets and bisimulation
AbstractSeveral categorical relationships (adjunctions) between models for concurrency have been established, allowing the translation of concepts and properties from one model to another. A central example is a coreflection between Petri nets and asynchronous transition systems. The purpose of the present paper is to illustrate the use of such relationships by transferring to Petri nets a general concept of bisimulation
Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets
We propose a framework for the specification of behaviour-preserving
reconfigurations of systems modelled as Petri nets. The framework is based on
open nets, a mild generalisation of ordinary Place/Transition nets suited to
model open systems which might interact with the surrounding environment and
endowed with a colimit-based composition operation. We show that natural
notions of bisimilarity over open nets are congruences with respect to the
composition operation. The considered behavioural equivalences differ for the
choice of the observations, which can be single firings or parallel steps.
Additionally, we consider weak forms of such equivalences, arising in the
presence of unobservable actions. We also provide an up-to technique for
facilitating bisimilarity proofs. The theory is used to identify suitable
classes of reconfiguration rules (in the double-pushout approach to rewriting)
whose application preserves the observational semantics of the net.Comment: To appear in "Logical Methods in Computer Science", 41 page
A Congruence for Petri Nets
We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our results are similar to the recent work by Milner on applying the theory of bigraphs to Petri Nets. The two main differences are that we treat p/t nets instead of c/e nets and we deal directly with a category of nets instead of encoding them into bigraphs
An Operational Petri Net Semantics for the Join-Calculus
We present a concurrent operational Petri net semantics for the
join-calculus, a process calculus for specifying concurrent and distributed
systems. There often is a gap between system specifications and the actual
implementations caused by synchrony assumptions on the specification side and
asynchronously interacting components in implementations. The join-calculus is
promising to reduce this gap by providing an abstract specification language
which is asynchronously distributable. Classical process semantics establish an
implicit order of actually independent actions, by means of an interleaving. So
does the semantics of the join-calculus. To capture such independent actions,
step-based semantics, e.g., as defined on Petri nets, are employed. Our Petri
net semantics for the join-calculus induces step-behavior in a natural way. We
prove our semantics behaviorally equivalent to the original join-calculus
semantics by means of a bisimulation. We discuss how join specific assumptions
influence an existing notion of distributability based on Petri nets.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
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