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19
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 22 (10 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.
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
Characterizing behavioural congruences for Petri nets
 Proc. CONCUR’95, LNCS 962
, 1995
"... Abstract. 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 corresp ..."
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Cited by 13 (3 self)
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Abstract. 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.
Representation Theorems for Petri Nets
 Foundations of Computer Science: Potential  Theory  Cognition, to Wilfried Brauer on the occasion of his sixtieth birthday, volume 1337 of Lect. Notes in Comp. Science
"... . This paper retraces, collects, summarises, and mildly extends the contributions of the authors  both together and individually  on the theme of representing the space of computations of Petri nets in its mathematical essence. Introduction Among the semantics proposed for Petri nets [10] (se ..."
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Cited by 11 (10 self)
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. This paper retraces, collects, summarises, and mildly extends the contributions of the authors  both together and individually  on the theme of representing the space of computations of Petri nets in its mathematical essence. Introduction Among the semantics proposed for Petri nets [10] (see also [11, 13]), a relevant role is played by the various notions of process, e.g. [12, 5, 1], whose merit is to provide a faithful account of computations involving many different transitions and of the causal connections between the events occurring in computations. Bare process models, however, fail to bring to the foreground the algebraic structure of the space of computations of a net. Our interest, instead, resides on abstract models that capture the mathematical essence of such spaces, possibly axiomatically, roughly in the same way as a prime algebraic domain (or, equivalently, a prime event structure) models the computations of a safe net [9]. The research detailed in [6, 3, 4, 14,...
Chu spaces: Complementarity and Uncertainty in Rational Mechanics
, 1994
"... this paper will be realizations. The category of Boolean operations and their propertypreserving renamings is not selfdual since nonT 0 Chu spaces transpose to nonextensional ones. By the same reasoning the full subcategory consisting of T 0 operations, those with no properties a j b for distinct ..."
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Cited by 9 (0 self)
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this paper will be realizations. The category of Boolean operations and their propertypreserving renamings is not selfdual since nonT 0 Chu spaces transpose to nonextensional ones. By the same reasoning the full subcategory consisting of T 0 operations, those with no properties a j b for distinct variables a; b, is selfdual. This is a very important fact: it means that to every full subcategory C of this selfdual category we may associate its dual as the image of C under the selfduality. This associates sets to complete atomic Boolean algebras, Boolean algebras to Stone spaces, distributive lattices to StonePriestley posets, semilattices to algebraic lattices, complete semilattices to themselves, and so on for many other familiar [Joh82] and not so familiar (selfduality of finitedimensional vector spaces over GF (2)) instances of Stone duality We now illustrate the general idea with some examples.
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 9 (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...
Chu Spaces From the Representational Viewpoint
 Ann. Pure Appl. Logic
, 1998
"... We give an elementary introduction to Chu spaces viewed as a set of strings all of the same length. This perspective dualizes the alternative view of Chu spaces as generalized topological spaces, and has the advantage of substituting the intuitions of formal language theory for those of topology. 1 ..."
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Cited by 8 (0 self)
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We give an elementary introduction to Chu spaces viewed as a set of strings all of the same length. This perspective dualizes the alternative view of Chu spaces as generalized topological spaces, and has the advantage of substituting the intuitions of formal language theory for those of topology. 1 Background Chu spaces provide a simple, uniform, and wellstructured approach to the representation of objects that may possess algebraic, relational, or other structure, and that can transform into one another in ways that respect that structure. Chu spaces are simple by virtue of being merely a rectangular array, with no further machinery. They are uniform in the sense that all transformable objects, whether sets, groups, Boolean algebras, vector spaces, or manifolds, are representable by Chu spaces within the same framework, and hence can coexist in a single typeless universe of mathematical objects. And they are wellstructured in that this seemingly featureless universe in fact has a na...
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 nonsequential processes, via unfolding constructions, which provide formal relationships between nets and domain ..."
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Cited by 7 (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 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. 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...
Time and Information in Sequential and Concurrent Computation
 In Proc. Theory and Practice of Parallel Programming
, 1994
"... Time can be understood as dual to information in extant models of both sequential and concurrent computation. The basis for this duality is phase space, coordinatized by time and information, whose axes are oriented respectively horizontally and vertically. We fit various basic phenomena of computat ..."
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Cited by 5 (1 self)
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Time can be understood as dual to information in extant models of both sequential and concurrent computation. The basis for this duality is phase space, coordinatized by time and information, whose axes are oriented respectively horizontally and vertically. We fit various basic phenomena of computation, and of behavior in general, to the phase space perspective. The extant twodimensional logics of sequential behavior, the van Glabbeek map of branching time and true concurrency, eventstate duality and scheduleautomaton duality, and Chu spaces, all fit the phase space perspective well, in every case confirming our choice of orientation. 1 Introduction Our recent research has emphasized a basic duality between time and information in concurrent computation. In this paper we return to our earlier work on sequential computation and point out that a very similar duality is present there also. Our main goal here will be to compare concurrent and sequential computation in terms of this dua...