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Reactive Systems over Cospans
, 2005
"... The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of wellbehaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimi ..."
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Cited by 46 (2 self)
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The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of wellbehaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need to be constructed separately within each model. In this paper, we o#er a general construction of such bicolimits in a class of bicategories of cospans. The construction sheds light on as well as extends Ehrig and Konig's rewriting via borrowed contexts and opens the way to a unified treatment of several applications.
On the Semantics of Place/Transition Petri Nets
, 1992
"... Abstract. In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical “token game”, one can model the behaviour of Petri nets via nonsequential processes, via unfolding constructions, which provide formal relationships between nets an ..."
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Cited by 26 (12 self)
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Abstract. In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical “token game”, one can model the behaviour of Petri nets via nonsequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. More precisely, we introduce the new notion of decorated processes of Petri nets and we show that they induce on nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net N can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification.
Reactive Systems, Barbed Semantics, and the Mobile Ambients
"... Reactive systems, proposed by Leifer and Milner, represent a metaframework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules. Despite its applicability, reactive systems suffered so far from two main drawbacks. Fir ..."
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Cited by 22 (6 self)
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Reactive systems, proposed by Leifer and Milner, represent a metaframework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules. Despite its applicability, reactive systems suffered so far from two main drawbacks. First of all, no technique was found for recovering a set of inference rules, e.g. in the socalled SOS style, for describing the distilled observational semantics. Most importantly, the efforts focussed on strong bisimilarity, tackling neither weak nor barbed semantics. Our paper addresses both issues, instantiating them on a calculus whose semantics is still in a flux: Cardelli and Gordon’s mobile ambients. While the solution to the first issue is tailored over our case study, we provide a general framework for recasting (weak) barbed equivalence in the reactive systems formalism. Moreover, we prove that our proposal captures the behavioural semantics for mobile ambients proposed by Rathke and Sobociński and by Merro and Zappa Nardelli.
Models for Concurrency: Towards a Classification
 Theoretical Computer Science
, 1996
"... Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. In thi ..."
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Cited by 21 (0 self)
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Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. In this paper, we move a step towards a classification of models for concurrency based on the parameters above. Formally, we choose a representative of any of the eight classes of models obtained by varying the three parameters, and we study the formal relationships between using the language of category theory.
Labels from Reductions: Towards a General Theory
 In Algebra and Coalgebra in Computer Science, Calco ’05, volume 3629 of LNCS
, 2005
"... Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems. ..."
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Cited by 17 (3 self)
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Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems.
An axiomatization of the category of Petri net computations
 Math. Struct. in Comput. Sci
, 1998
"... Abstract. We introduce the notion of strongly concatenable process as a refinement of concatenable processes [3] which can be expressed axiomatically via a ..."
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Cited by 13 (5 self)
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Abstract. We introduce the notion of strongly concatenable process as a refinement of concatenable processes [3] which can be expressed axiomatically via a
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 12 (5 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.
Representations of Petri net interactions
"... We introduce a novel compositional algebra of Petri nets, as well as a stateful extension of the calculus of connectors. These two formalisms are shown to have the same expressive power. ..."
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Cited by 11 (5 self)
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We introduce a novel compositional algebra of Petri nets, as well as a stateful extension of the calculus of connectors. These two formalisms are shown to have the same expressive power.
A Behavioural Congruence for Web services
 In Arbab, F., Sarjani, M., eds.: Fundamentals of Software Engineering, LNCS (To appear
, 2007
"... Abstract. Web services are emerging as a promising technology for the development of next generation distributed heterogeneous software systems. We define a new behavioural equivalence for Web services, based on bisimilarity and inspired by recent advances in the theory of reactive systems. The prop ..."
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Cited by 10 (5 self)
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Abstract. Web services are emerging as a promising technology for the development of next generation distributed heterogeneous software systems. We define a new behavioural equivalence for Web services, based on bisimilarity and inspired by recent advances in the theory of reactive systems. The proposed equivalence is compositional and decidable, and it provides a firm ground for enhanced behaviouraware discovery and for a sound incremental development of services and service compositions. 1
On the Category of Petri Net Computations
, 1995
"... . We introduce the notion of strongly concatenable process as a refinement of concatenable processes [3] which can be expressed axiomatically via a functor Q[ ] from the category of Petri nets to an appropriate category of symmetric strict monoidal categories, in the precise sense that, for each ne ..."
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Cited by 10 (6 self)
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. We introduce the notion of strongly concatenable process as a refinement of concatenable processes [3] which can be expressed axiomatically via a functor Q[ ] from the category of Petri nets to an appropriate category of symmetric strict monoidal categories, in the precise sense that, for each net N , the strongly concatenableprocesses of N are isomorphic to the arrows of Q[N ]. In addition, we identify a coreflection right adjoint to Q[ ] and characterize its replete image, thus yielding an axiomatization of the category of net computations. Introduction Petri nets, introduced by C.A. Petri [8] (see also [10]), are unanimously considered among the most representative models for concurrency, since they are a fairly simple and natural model of concurrent and distributed computations. However, Petri nets are, in our opinion, not yet completely understood. Among the semantics proposed for Petri nets, a relevant role is played by the various notions of process [9, 4, 1], whose merit is...