Roberto Bruni and Ugo Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1-2):46-89, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of the place p in t. The post condition t of t similarly represents the edges exiting t. A marking M for N is a labeled multiset over P . Each element x:p in M is called a token. Our use of labels constitutes a departure, known as the individual token philosophy and analyzed in [BMMS98, BM00], from the de nition of markings and Petri nets commonly found in the literature. The implications are rather subtle: labels assign an identity to tokens inhabiting the same place, making it possible to distinguish them. Therefore, where the more traditional collective token approach prescribe ....

.... M pc2 for the producer consumer net (displayed in Figure 2) 1 b 4 ; r tok c tok n tok n tok n tok b tok b) It should be observed that this representation, and in particular the presence of labels, is a direct implementation of the individual token approach to Petri nets [BMMS98, BM00]. This derives from the fact that CLF, like most logical frameworks, forces every assumption to have a unique name. An extension of CLF with proof irrelevance [Pfe01a] would avoid this arti ciality, allowing a direct representation of the collective token philosophy . We intend to investigate ....

Roberto Bruni and Ugo Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1-2):46{ 89, 2000.

....occurrences of the place p in . t. The post condition t . of t similarly represents the edges exiting t. A marking M for N is a labeled multiset over P . Each element x:p in M is called a token. Our use of labels constitutes a departure, known as the individual token philosophy and analyzed in [BMMS98, BM00], from the definition of markings and Petri nets commonly found in the literature. The implications are rather subtle: labels assign an identity to tokens inhabiting the same place, making it possible to distinguish them. Therefore, where the more traditional collective token approach prescribe ....

.... producer consumer net (displayed in Figure 2) b 4 , r# tok c# tok n# tok n# tok n# tok b# tok b) It should be observed that this representation, and in particular the presence of labels, is a direct implementation of the individual token approach to Petri nets [BMMS98, BM00]. This derives from the fact that CLF, like most logical frameworks, forces every assumption to have a unique name. An extension of CLF with proof irrelevance [Pfe01a] would avoid this artificiality, allowing a direct representation of the collective token philosophy . We intend to investigate ....

Roberto Bruni and Ugo Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1--2):46-- 89, 2000.

.... 58] Milano WFMS [10] Next, we have looked at Petri net variants that are not specifically tailored towards workflow modelling but nevertheless can be useful: Open Nets [16] Petri nets with synchronous communication [37] Signal Event Nets [87, 70] Contextual Nets [128, 72] Zero Safe nets [27], and several variants of Object Oriented Petri Nets [9, 121] More information about some of these references can be found in recent overviews and collections about the use of Petri nets for workflow modelling [1, 144] A comparison of our semantics with other (formal) modelling techniques can be ....

....latter semantics any sequence of transitions, obeying the firing rules, is allowed. So, it could be possible that under the standard Petri semantics an event lives longer than a step, i.e. is not removed after it has been responded to. Recently, a new Petri net variant, called zero safe nets [27], has been proposed that seems a good starting point for modelling the statechart step semantics. In zero safe nets, some places, called zero places, represent unobservable system states. A marking in which one or more zero places are filled is unstable, otherwise it is stable. During execution, ....

R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1-2):46--89, 2000.

....example, tile models for most process algebras (Gadducci and Montanari 2000) have process terms as con gurations, and elements of the free monoid of actions (which are unary symbols) as observations. The simplest possible interpretation of structured con gurations and observations is considered in (Bruni and Montanari 2000), and consists in P T net markings. As an important result, horizontal composition in the tile model yields a notion of transition synchronization, an important feature for compositionality, which is missing in ordinary nets (where only token synchronization is provided) and usually achieved ....

Bruni, R. and Montanari, U. (2000) Zero-Safe Nets: Comparing the Collective and Individual Token Approaches. Information and Computation 156, 46-89. Academic Press.

....by tile logic is suitable to deal with structural axioms on the algebra of con gurations and open ended system speci cations, allowing for a nitary presentation of context closure. The theoretical foundation for a class of simple tile models, called zerosafe nets, has been investigated in [BM00b] together with the application to several case studies. In zero safe nets, both system con gurations and e ects are represented as multisets of basic elements. They extend Petri nets with the notion of transaction atomic computation obtained via the synchronization mechanism and can provide a ....

R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156:46-89, 2000.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156:46-89, 2000.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comp., 1999. to appear.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156(1-2):46-89, 2000.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156:46--89, 2000. http://www. idealibrary.com/links/toc/inco/156/1/0

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156(1-2):46--89, 2000.

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Bruni, R. and U. Montanari, Zero-safe nets: Comparing the collective and individual token approaches, Inform. and Comput. 156 (2000), pp. 46--89.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156(1-2):46--89, 2000.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156(1-2):46--89, 2000.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156(1-2):46-89, 2000.

.... boxes correspond to a two level classification of states, observable (i.e. outside the box) and hidden (i.e. inside the box) This partition also pervades another formalism, which has been recently defined to model transactional aspects in concurrent systems, the zero safe Petri nets (ZS nets) [5, 7]. Actually, BizTalk flowcharts may be easily encoded into ZS nets, while the converse encoding seems not possible. The reason is that BizTalk boxes provide a somewhat static specification of transactions A transaction can be considered as a collection of actions with the following properties: ....

....kinds of transactions, i.e. long running and timed, which rely on user defined compensation code. 2. 1 BizTalk without boxes BizTalk flowcharts may be converted into a standard formalism for concurrent computations, the Petri nets; actually into a transactional flavour of them, the zero safe nets [5]. We split this conversion into two steps: in the first step we draw transaction in a different manner dropping boxes; in the second step we introduce states. First step: coloring basic shapes. In BizTalk, transactions are depicted by grouping basic shapes into (shadowed) boxes (Figures 1(b) and ....

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156(1-2):46--89, 2000.

....their usage too far (employing categories in a mild way) and shall give informal explanations of most categorical constructs introduced. Likewise context systems (Larsen Xinxin, 1990) and conditional transition systems (Rensink, 2000) tile logic allows one to reason about terms with variables (Bruni et al. 2000a) This means, e.g. that trace semantics and bisimilarity can be extended straightforwardly to open terms by taking as observation the pair htrigger; effecti, whereas ordinary LTS s deal with transitions from closed terms to closed terms for which triggers are trivial identities. The ....

....LTS s deal with transitions from closed terms to closed terms for which triggers are trivial identities. The compositionality of abstract semantics (either based on traces or on bisimilarity) can then be guaranteed by algebraic properties of the tile system or by suitable specification formats (Bruni et al. 2000a) In particular, we shall see that the decomposition property (Gadducci Montanari, 2000) yields a very simple proof of the compositionality of the tile logic associated to a logic program. The tile approach to logic programming A well known fact (cf. the discussion in Section 2 and ....

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Bruni, R., & Montanari, U. (2000). Zero-safe nets: Comparing the collective and individual token approaches. Inform. and comput., 156, 46--89.

.... by suitable monoidal double categories [25, 10] nor the axiomatized proof terms decorating tile sequents [25, 8] Varying the algebraic structure of configurations and observations, tiles can model many different aspects of dynamic systems, ranging from synchronization of Petri net transitions [12], to causal dependencies for located calculi and finitely branching representations for name passing calculi [23] In addition, tile logic allows reasoning about terms with variables in the style of Larsen and Xinxin s context systems [28] or Rensink s conditional transition systems [40] while ....

R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156:46--89, 2000.

....[s M ] s M 0 ] 0 1 is entailed by RN . Alternatively, the multiset structure of markings could be recovered by considering each place as an operation with source and target 0, and then analyzing its associated monoidal theory; this is reflected in the presentation of zero safe nets [14] given by Roberto Bruni and Ugo Montanari. Likewise, also the firing step semantics could be recovered extending the rewriting logic paradigm to monoidal theories; we defer such an extension to Section 3.3. 3.2.2 Encoding substitution: on the calculus As Petri nets represent a foundational ....

R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156:46--89, 2000.

....logic (expressed by suitable monoidal double categories [12,6] nor the axiomatized proof terms decorating tile sequents. Varying the algebraic structure of con gurations and observations tiles can model many di erent aspects of dynamic systems, ranging from synchronization of net transitions [7], to causal dependencies for located calculi and nitely branching approaches for name passing calculi [11] to actor systems [21] In addition, tile logic allows one to reason about terms with variables as Larsen and Xinxin s context systems [14] while sos formats work for ground terms only. ....

R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156:46-89, 2000.

....nets can favor a uniform approach to concurrent languages translation. For instance, in the case of ccs like process algebras, the parallel composition of two nets modeling communicating processes involves the combinatorial analysis of all the admissible synchronizations, whereas we have shown in [15] that by using zero places for 3 modeling communication channels, then the parallel composition of two nets can just merge the common channels. As an original contribution, here we show how to model distributed choices in a compositional way and discuss how the basic concept of zero place can ....

....avours, still preserving some distinguishing features of the approach. For what concerns zs nets implementation, one has to specify the computational machinery for performing only correct transactions, recovering deadlocks and treating in nite low level computations. We illustrate our proposal of [15] for equipping zs nets with such a distributed operational tool and then extend it to deal with read arcs in contextual (zero safe) nets. Origin and structure of the paper. The operational and abstract semantics of zs nets according to the two more di used net philosophies (called collective token ....

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156:46-89. Academic Press, 2000.

....view, which corresponds to the abstraction from the mechanism for supervising the atomic production and consumption of zero tokens. This mechanism provides a unique computational strategy, which is expressive enough to model, e.g. a multicasting system and simple process algebras (cf. [7,12]) We remark that the notions of atomicity and evaluation strategy required by the methodology for designing systems via re nement, are built in inside the zs net model itself. The operational and abstract semantics of zs nets according to the two more di used net philosophies (called ....

....philosophies (called collective token and individual token) have been presented in [10,11] where it is shown that they can be formulated as universal constructions in the language of category theory. A comparison between the two approaches together with several applications has been discussed in [12] and in the Ph.D. Thesis of rst author [7] A tutorial presentation of the material can be found in [13] We focus here on a distributed interpreter for zs nets. Dining Philosophers and Free Choice Nets. A simple example that ts well the situation discussed so far can be illustrated by modeling ....

R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Inform. and Comput., 156:46-89. Academic Press, 2000.

....can be defined (by assuming a labeling of net transitions) In this paper, apart from the classical token game, we will mainly rely on the (deterministic) process approach. For the algebraic account of the operational and abstract semantics of zs nets, here summarized in Section 4, we refer to [10]. Some proposal for the unfolding semantics will be discussed in Section 5. Collective and individual token philosophies Since the concurrent semantics of an operational model considers as equivalent all the computations where the same concurrent events are executed in different orders, it is ....

....actual order of execution of concurrent transitions in the refined net is invisible in the abstract net, but all the causal dependencies are preserved. The multicasting system example To better illustrate the concepts so far discussed, we describe a simple but enlightening example, taken from [10]. We start by considering the zs net MS pictured in Figure 4. The net MS is designed to model a multicasting system: As in a broadcasting system, an agent can simultaneously send the same message to an unlimited number of receivers, but here the receivers are not necessarily all the remaining ....

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R. Bruni and U. Montanari, Zero-safe nets: Comparing the collective and the individual token approaches, Information and Computation, to appear.

.... freely) This feature of tile logic has been at the basis of several successful application as a model of computation for reactive systems: varying the algebraic structures of configurations and observations many different aspects can be modelled, ranging from synchronization of net transitions [7], to causal dependencies for located calculi [16] to finitely branching approaches for namepassing calculi [15] to actor systems [34] Moreover, tile logic allows one to reason about open configurations, in the style of context systems [21] whilst ordinary SOS formats work for ground terms only ....

....the algebra of configurations, is then lifted to tiles (in the horizontal dimension only) whilst the observations just yield a monoid over the sequences of basic actions. Within this class we recall a net model equipped with a synchronization mechanism between transitions, called zero safe nets [7]. This is probably the simplest tile model one can imagine, because its configurations and its observations are just commutative monoids (the monoidal operation models both parallel and sequential compositions) Other examples consist of the monoidal tile system for finite CCS of [30] where ....

R. Bruni and U. Montanari, Zero-Safe Nets: Comparing the Collective and the Individual Token Approaches, Information and Computation, to appear.

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Roberto Bruni and Ugo Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1-2):46-89, 2000.

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Roberto Bruni and Ugo Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1-2):46{ 89, 2000.

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Roberto Bruni and Ugo Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1--2):46--89, 2000.

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R. Bruni and U. Montanari (2000), Zero-Safe Nets: Comparing the Collective and Individual Token Approaches. Information and Computation 156 46--89, Academi Press.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1-2):46--89, 2000.

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R. Bruni and U. Montanari (2000), Zero-Safe Nets: Comparing the Collective and Individual Token Approaches. Information and Computation 156 46--89, Academi Press.

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Roberto Bruni and Ugo Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1--2):46--89, 2000.

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R. Bruni and U. Montanari. Zero-safe nets: Comparing the collective and individual token approaches. Information and Computation, 156(1-2):46-89, 2000.

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