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Bisimilarity and BehaviourPreserving Reconfigurations of Open Petri Nets
"... We propose a framework for the specification of behaviourpreserving 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 ..."
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Cited by 10 (4 self)
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We propose a framework for the specification of behaviourpreserving 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 colimitbased composition operation. We show that natural notions of (strong and weak) bisimilarity over open nets are congruences with respect to the composition operation. We also provide an upto technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the doublepushout approach to rewriting) whose application preserves the observational semantics of the net.
On Concurrent Realization of Reactive Systems and Their Morphisms
 Advances in Petri Nets: Unifying Petri Nets, LNCS
, 2001
"... Abstract. The paper introduces the notion of concurrent realization of reactive systems. A framework is also presented in which labelled safe Petri nets as concurrent realizations of concrete asynchronous systems are constructed. The construction is uniform in the sense that it extends to a realizat ..."
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Cited by 6 (3 self)
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Abstract. The paper introduces the notion of concurrent realization of reactive systems. A framework is also presented in which labelled safe Petri nets as concurrent realizations of concrete asynchronous systems are constructed. The construction is uniform in the sense that it extends to a realization of an arbitrary diagram. We discuss applicability of the framework to construct maximally concurrent realizations of reactive systems. 1
Finite Completeness of Categories of Petri Nets
, 2000
"... . The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equalizers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not ..."
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Cited by 4 (2 self)
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. The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equalizers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not finitely complete. The main positive result of the paper states that reachable Petri nets with multiplicative morphisms form a finitely complete category. As an application of this result, some wellknown categories are shown to be finitely complete. For instance, since all morphisms between reachable safe Petri nets are multiplicative, it follows that the category of reachable safe Petri nets is finitely complete. Keywords: Categories of Petri nets, products, equalizers, (finite) completeness. 1. Introduction Studies of categorytheoretical foundations of concurrent processes and their models go back to the work of Winskel in the 80s, see [15] for an account of the work done in this area....
Unfolding Semantics of Graph Transformation 1
"... Several attempts have been made of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets, but only partial results were obtained. In this paper we fully extend Winskel’s approach to singlepushout grammars providing them with a categorical concurre ..."
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Several attempts have been made of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets, but only partial results were obtained. In this paper we fully extend Winskel’s approach to singlepushout grammars providing them with a categorical concurrent semantics expressed as a
Abstraction and Abstraction Refinement in the Verification of Graph Transformation Systems
"... Graph transformation systems (GTSs) form a natural and convenient specification language which is used for modelling concurrent and distributed systems with dynamic topologies. These can be, for example, network and Internet protocols, mobile processes with dynamic behavior and dynamic pointer struc ..."
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Graph transformation systems (GTSs) form a natural and convenient specification language which is used for modelling concurrent and distributed systems with dynamic topologies. These can be, for example, network and Internet protocols, mobile processes with dynamic behavior and dynamic pointer structures in programming languages. All this, together with the possibility to visualize and explain system behavior using graphical methods, makes GTSs a wellsuited formalism for the specification of complex dynamic distributed systems. Under these circumstances the problem of checking whether a certain property of GTSs holds – the verification problem – is considered to be a very important question. Unfortunately the verification of GTSs is in general undecidable because of the Turingcompleteness of GTSs. In the last few years a technique for analysing GTSs based on approximation by Petri graphs has been developed. Petri graphs are Petri nets having additional graph structure. In this work we focus on the verification techniques based on counterexampleguided abstraction refinement (CEGAR approach). It starts with a coarse initial overapproximation