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Configuration Structures, Event Structures and Petri Nets
"... In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without self-loops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive powe ..."
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Cited by 12 (1 self)
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In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without self-loops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive power of such nets. These new event structures and nets are connected by relating both notions with configuration structures, which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them, but abstract from any auxiliary structure. A configuration structure can also be considered logically, as a class of propositional models, or—equivalently— as a propositional theory in disjunctive normal from. Converting this theory to conjunctive normal form is the key
Concurrent Computing: from Petri Nets to Graph Grammars
- Electronic Notes in Theoretical Computer Science
, 1995
"... Petri nets are widely accepted as a specification formalism for concurrent and distributed systems. One of the reasons of their success is the fact that they are equipped with a rich theory, including well-understood concurrent semantics; they also provide an interesting benchmark for tools and tech ..."
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Cited by 10 (0 self)
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Petri nets are widely accepted as a specification formalism for concurrent and distributed systems. One of the reasons of their success is the fact that they are equipped with a rich theory, including well-understood concurrent semantics; they also provide an interesting benchmark for tools and techniques for the description of concurrent systems. Graph grammars can be regarded as a proper generalization of Petri nets, where the current state of a system is described by a graph instead as by a collection of tokens. In this tutorial paper I will review some basic definitions and constructions concerning the concurrent semantics of nets, and I will show to what extent corresponding notions have been developed for graph grammars. Most of such results come out from a joint research by the Berlin and Pisa COMPUGRAPH groups. 1 Introduction The nets which owe their name to Carl Adam Petri [28,29] have been the first formal tool proposed for the specification of the behaviour of systems which...
Configuration Structures (Extended Abstract)
- Proceedings 10 th Annual IEEE Symposium on Logic in Computer Science, LICS’95
, 1995
"... Configuration structures provide a model of concurrency generalising the families of configurations of event structures. They can be considered logically, as classes of propositional models; then sub-classes can be axiomatised by formulae of simple prescribed forms. Several equivalence relations for ..."
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Cited by 10 (7 self)
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Configuration structures provide a model of concurrency generalising the families of configurations of event structures. They can be considered logically, as classes of propositional models; then sub-classes can be axiomatised by formulae of simple prescribed forms. Several equivalence relations for event structures are generalised to configuration structures, and also to general Petri nets. Every configuration structure is shown to be ST-bisimulation equivalent to a prime event structure with binary conflict; this fails for the tighter history preserving bisimulation. Finally, Petri nets without self-loops under the collective token interpretation are shown behaviourally equivalent to configuration structures, in the sense that there are translations in both directions respecting history preserving bisimulation. This fails for nets with self-loops. 1 Introduction The aim of this paper is to connect several models of concurrency, by providing translations between them and studying whi...
Unfolding of double-pushout graph grammars is a coreflection
- PROCEEDINGS INTERNATIONAL WORKSHOP ON THEORY AND APPLICATION OF GRAPH TRANSFORMATIONS, VOLUME 1764 OF LECT. NOTES IN COMP. SCI
, 1999
"... In a recent paper, mimicking Winskel’s construction for Petri nets, a concurrent semantics for (double-pushout) DPO graph grammars has been provided by showing that each graph grammar can be unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar d ..."
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Cited by 9 (7 self)
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In a recent paper, mimicking Winskel’s construction for Petri nets, a concurrent semantics for (double-pushout) DPO graph grammars has been provided by showing that each graph grammar can be unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. This paper faces the problem of providing a closer correspondence with Winskel’s result by showing that the unfolding construction can be described
On the Model of Computation of Place/Transition Petri Nets
, 1994
"... . 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 non-sequential processes, via unfolding constructions, which provide formal relationships between nets ..."
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Cited by 9 (2 self)
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. 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 non-sequential 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. Introduction Petri nets, introduced by C.A. Petri in [18] (see also [21]), are a widely used model of concurrency. This model is attractive from a theoretical po...
Zero-Safe Nets: Composing Nets via Transition Synchronization
- Proceedings Int. Colloquium on Petri Net Technologies for Modelling Communication Based Systems
, 1999
"... Zero-safe nets have been introduced to extend classical Petri nets with a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable, zero-safe nets are equipped with zero places, which cannot contain any token in a stable marking . An evolution between two s ..."
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Cited by 4 (3 self)
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Zero-safe nets have been introduced to extend classical Petri nets with a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable, zero-safe nets are equipped with zero places, which cannot contain any token in a stable marking . An evolution between two stable markings is called transaction and can be a complex computation that involves zero places, with the restriction that no stable token generated in a transaction can be reused in the same transaction. The abstract counterpart of a generic zerosafe net B consists of an ordinary pt net whose places are the stable places of B, and whose transitions are the transactions of B. The two nets offer the refined and the abstract model of the same system, where the former can be much smaller than the latter, because of the transition synchronization mechanism. Depending on the chosen approach --- collective vs individual token philosophy --- two notions of transaction may be defined, each leading ...
Unfolding graph transformation systems: Theory and applications to verification
- In Concurrency, Graphs and Models: Essays Dedicated to Ugo Montanari on the Occasion of His 65th Birthday
, 2008
"... Abstract. The unfolding of a system represents in a single branching structure all its possible computations: it is the cornerstone both of se-mantical constructions and of efficient partial order verification tech-niques. In this paper we survey the contributions we elaborated in the last decade wi ..."
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Cited by 3 (0 self)
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Abstract. The unfolding of a system represents in a single branching structure all its possible computations: it is the cornerstone both of se-mantical constructions and of efficient partial order verification tech-niques. In this paper we survey the contributions we elaborated in the last decade with Ugo Montanari and other colleagues, concerning the unfolding of graph transformation systems, and its use in the defini-tion of a Winskel style functorial semantics and in the development of methodologies for the verification of finite and infinite state systems. 1
unknown title
"... Abstract Processes of timed Petri nets are represented by labelled partial orders with some extra features. These features reflect the execution times of processes and allow to combine processes sequentially and in parallel. The processes can be represented either without specifying when particular ..."
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Abstract Processes of timed Petri nets are represented by labelled partial orders with some extra features. These features reflect the execution times of processes and allow to combine processes sequentially and in parallel. The processes can be represented either without specifying when particular situations appear (free time-consuming processes), or together with the respective appearance times (timed time-consuming processes). The processes of the latter type determine the possible firing sequences of the respective nets.
