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Contextual petri nets, asymmetric event structures and processes
 Information and Computation
, 2001
"... We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (readonly operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structure ..."
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Cited by 42 (16 self)
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We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (readonly operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskel’s seminal work on safe nets, the truly concurrent event based semantics of contextual nets is given at categorical level via a chain of coreflections
Unfolding and Event Structure Semantics for Graph Grammars
 PROCEEDINGS OF THE 5TH INTERNATIONAL WORKSHOP ON GRAPH GRAMMARS AND THEIR APPLICATION TO COMPUTER SCIENCE, VOLUME 1073 OF LNCS
, 1996
"... We propose an unfolding semantics for graph transformation systems in the doublepushout (DPO) approach. Mimicking Winskel’s construction for Petri nets, a graph grammar is unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the ..."
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Cited by 38 (24 self)
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We propose an unfolding semantics for graph transformation systems in the doublepushout (DPO) approach. Mimicking Winskel’s construction for Petri nets, a graph grammar is unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. The unfolding can be abstracted naturally to a prime algebraic domain and then to an event structure semantics. We show that such event structure coincides both with the one defined by Corradini et al. [3] via a
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.
Concatenable graph processes: relating processes and derivation traces
 IN PROCEEDINGS OF ICALP’98, VOLUME 1443 OF LNCS
, 1998
"... Several formal concurrent semantics have been proposed for graph rewriting, a powerful formalism for the specification of concurrent and distributed systems which generalizes P/T Petri nets. In this paper we relate two such semantics recently proposed for the algebraic doublepushout approach to gra ..."
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Cited by 19 (15 self)
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Several formal concurrent semantics have been proposed for graph rewriting, a powerful formalism for the specification of concurrent and distributed systems which generalizes P/T Petri nets. In this paper we relate two such semantics recently proposed for the algebraic doublepushout approach to graph rewriting, namely the derivation trace and the graph process semantics. The notion of concatenable graph process is
ZeroSafe Nets, or Transition Synchronization Made Simple
 PROC. OF EXPRESS’97
, 1997
"... In addition to ordinary places, called stable, zerosafe nets are equipped with zero places, which in a stable marking cannot contain any token. An evolution between two stable markings, instead, can be a complex computation called stable transaction, which may use zero places, but which is atomic w ..."
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Cited by 17 (13 self)
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In addition to ordinary places, called stable, zerosafe nets are equipped with zero places, which in a stable marking cannot contain any token. An evolution between two stable markings, instead, can be a complex computation called stable transaction, which may use zero places, but which is atomic when seen from stable places: no stable token generated in a transaction can be reused in the same transaction. Every zerosafe net has an ordinary PlaceTransition net as its abstract counterpart, where only stable places are maintained, and where every transaction becomes a transition. The two nets allow us to look at the same system from both an abstract and a refined viewpoint. To achieve this result no new interaction mechanism is used, besides the ordinary tokenpushing rules of nets. The refined zerosafe nets can be much smaller than their corresponding abstract P/T nets, since they take advantage of a transition synchronization mechanism. For instance, when transactions of unlimited l...
Transactions and ZeroSafe Nets
 Advances in Petri Nets: Unifying Petri Nets, Lect. Notes in Comput. Sci. 2128
, 2001
"... When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transac ..."
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Cited by 16 (8 self)
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When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transactions based on zerosafe nets. They extend ordinary pt nets with a simple mechanism for transition synchronization. We show that the net theory developed under the two most diffused semantic interpretations (collective token and individual token philosophies) can be uniformly adapted to zerosafe nets. In particular, we show that each zerosafe net has associated two pt nets which represent the abstract counterparts of the modeled system according to the two philosophies. We show several applications of the framework, a distributed interpreter for zs nets based on classical net unfolding (here extended with a commit rule) and discuss some extensions to other net flavours.
A comparison of Petri net semantics under the collective token philosophy
 SpringerVerlag LNCS
, 1998
"... Abstract. In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric ..."
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Cited by 15 (9 self)
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Abstract. In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. Weusethenotionof adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic.
ZeroSafe Nets: The Individual Token Approach
 Proceedings WADT'97, 12th workshop on Recent Trends in Algebraic Development Techniques, volume 1376 of Lect. Notes in Comput. Sci
, 1998
"... In this paper we provide both an operational and an abstract concurrent semantics for zerosafe nets under the individual token philosophy. The main feature of zerosafe nets is a primitive notion of transition synchronization. Besides ordinary places, called stable places, zerosafe nets come equip ..."
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Cited by 13 (13 self)
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In this paper we provide both an operational and an abstract concurrent semantics for zerosafe nets under the individual token philosophy. The main feature of zerosafe nets is a primitive notion of transition synchronization. Besides ordinary places, called stable places, zerosafe nets come equipped with zero places, which are empty in any stable marking. Connected transactions represent basic atomic computations of the system between stable markings. They must satisfy two main requirements: 1) to model interacting activities which cannot be decomposed into disjoint subactivities, and 2) not to consume stable tokens which were generated in the same transaction. Zero tokens acts as triggers for the firings of the transitions which compose the transaction. The abstract counterpart of a zerosafe net consists of a P/T net where each transition locates a distinguished transaction. In the second part of the paper, following the Petri nets are monoids approach, we make use of catego...
Domain and Event Structure Semantics for Petri Nets with Read and Inhibitor Arcs
"... We propose a functorial concurrent semantics for Petri nets extended with read and inhibitor arcs, that we call inhibitor nets. Along the lines of the seminal work by Winskel on safe (ordinary) nets, the truly concurrent semantics is given at a categorical level via a chain of coreflections leading ..."
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Cited by 13 (5 self)
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We propose a functorial concurrent semantics for Petri nets extended with read and inhibitor arcs, that we call inhibitor nets. Along the lines of the seminal work by Winskel on safe (ordinary) nets, the truly concurrent semantics is given at a categorical level via a chain of coreflections leading from the category SWIN of semiweighted inhibitor nets to
Functorial Semantics for Petri Nets under the Individual Token Philosophy
, 1999
"... Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lac ..."
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Cited by 12 (10 self)
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Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of prenet to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of nets.