F. Gadducci and U. Montanari (1998), Axioms for contextual net processes, Proceedings of ICALP 98, K. Larsen et al. (Eds.), Lecture Notes in Computer Science 1443, 296--308, Springer-Verlag.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....as well. The result generalizes Winskel s 8 seminal work on safe nets, making use of the original notion of Asymmetric Event Structure. These notions and results about contextual nets can be seen as a first step towards the definition of an unfolding semantics for graph grammars. The paper [GM98a] lays the basis for a characterization of processes of contextual P T nets as arrows of a suitable category. First, the class of contextual processes of a net is defined; then, it is shown how these processes can be modeled as arrows of a monoidal category, enriched with operators allowing for a ....

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Proceedings ICALP'98, LNCS. Springer Verlag, 1998. To appear. 23

....nets both the process and the unfolding approaches have been studied [27,8,9,2,1] giving a satisfactory understanding of the computational model via the introduction of asymmetric event structures. The algebraic approach, however, has been pursued only in a recent paper by Gadducci and Montanari [16] using matchshare categories. Their basic idea is that, together with symmetries, two additional auxiliary constructors must be present: one for duplicating tokens and one for matching them. Formally, for each place a the auxiliary arrows a : a a a and D a : a a a are added to the ....

....copy with the corresponding produced tokens (i.e. by considering the arrow b t v = id u v ) t v id v ) id w D v ) illustrated in Figure 2(a) Multiple concurrent access is achieved by producing via duplication and then absorbing via matching enough copies of the context. In [16], a suitable axiomatization of duplicators and matchers is introduced and proved to represent faithfully the basic fact about concurrent access: steps sharing the same context, but otherwise disjointly enabled, can execute concurrently or in any interleaved order with no noticeable difference ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Proc. ICALP'98, 25th International Colloquium on Automata, Languages, and Programming, (K.G. Larsen, S. Skyum, G. Winskel, Eds.), vol. 1443 of Lect. Notes in Comput. Sci., pp. 296--308. Springer, 1998.

....nets both the process and the unfolding approaches have been studied [13,1] giving a satisfactory understanding of the computational model via the introduction of asymmetric event structures. The algebraic approach, however, has been pursued only in a recent paper by Gadducci and Monta nari [6] using match share categories. There, the basic idea is that, together with symmetries, two additional auxiliary constructors must be present: one for duplicating tokens and one for matching them. Read arcs can then be replaced by self loops, and reading without consuming modeled by duplicating ....

....the context, ring the transition concurrently with an idle copy of the context, and then matching the idle copy with the corresponding produced tokens. Multiple concurrent access is achieved by producing via duplication and then absorbing via matching enough copies of the context. In [6] a suitable axiomatization of duplicators and matchers is introduced and proved to represent faithfully the basic fact about concurrent access: steps sharing the same context, but otherwise disjointly enabled, can execute concurrently or in any interleaved order with no noticeable di erence. The ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Proc. ICALP'98, vol. 1443 of Lect. Notes in Comput. Sci., pp. 296-308. Springer, 1998.

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F. Gadducci and U. Montanari. Axioms for contextual net processes. Proc. ICALP'98, LNCS 1443, pp. 296--308. Springer, 1996.

No context found.

F. Gadducci and U. Montanari. Axioms for contextual net processes. Proc. ICALP'98, LNCS 1443, pp. 296--308. Springer, 1996.

No context found.

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Proceedings of ICALP'98, 25th International Colloquium on Automata, Languages and Programming, volume 1443 of Lect. Notes in Comput. Sci., pages 296--308. Springer Verlag, 1996.

....sort of data matching. Analogously, codischargers are introduced to represent the explicit creation of data. Several combinations are then possible, where only some of the operators are considered, and their mixed compositions are di erently axiomatized, ranging from the match share categories of [17] to the dgs monoidal categories of [15,16,22] We sketch now a survey of the topic, brie y commenting their role in the literature and the main di erences between similar models. We start with what we call an r monoidal category: One of the various extensions, albeit with a di erent name, ....

.... functor F : C C 0 is a share functor (with respect to r) such that also F op : C op C 0op is so (with respect to op ) We denote by MShCat the category of match share categories (as objects) and match share functors (as arrows) Match share categories have been used in [17] to embed the algebraic properties of processes for contextual nets [31] and, more generally, they can be considered as models for partition based structures. We talk about partitions because, in the set theoretical interpretation, the axioms on the additional operators enforce a sort of ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. Axioms for contextual net processes. In K.G. Larsen, S. Skyum, and G. Winskel, editors, Proc. of ICALP'98, Automata, Languages and Programming, volume 1443 of Lect. Notes in Comp. Science, pages 296-308. Springer Verlag, 1998.

....of data matching. Analogously, co dischargers are introduced to represent the explicit creation of data. Several combinations are then possible, where only some of the operators are considered, and their mixed compositions are differently axiomatized, ranging from the match share categories of [14] to the dgs monoidal categories of [13, 18] Here we just sketch a survey of the categorical framework, and briefly comment their role in the literature and the main differences between similar models. We start with what we call a r monoidal category: One of the various extensions, albeit with a ....

....a Omega a a Omega Delta a a Omega a a ra a E E E E E E a Omega a fflffl Delta a a A match share functor F : C Gamma C 0 is a share functor such that also F op is so. We denote by MShCat the category of match share functors. Match share categories have been introduced in [14], and used to embed the algebraic properties of processes for contextual nets [25] They are the basis for a class of categories where suitable models of partition based structures can live. Definition 7 (Part Monoidal Categories) A part monoidal category is an 8 tuple hC; Omega ; e; fl; r; ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Automata, Languages and Programming, volume 1443 of LNCS, pages 296--308. Springer Verlag, 1998.

....paper [18] for an extensive discussion on the usefulness of category theory in computer science. Relation with deterministic processes. The problem of providing a truly concurrent semantics for contextual nets based on (deterministic) processes has been faced by various authors (see, e.g. [28, 17, 19, 9, 36, 38]) Each deterministic process of a contextual net records the events occurring in a single computation of the net and the relationships existing between such events. Clearly, since the unfolding of a net is essentially a nondeterministic process that completely describes the behaviour of the net, ....

.... for the net N is introduced, where objects are markings (states of the net) arrows are (decorated) processes (computations of the net) and arrow composition is an operation of concatenation of processes consistent with causal dependencies, modelling sequential composition of computations [17, 38]. Then the comma category (m # CP[N ] where m is the initial marking of the net, is shown to be a preorder, inducing a partial order whose ideal completion is isomorphic to the domain associated to the unfolding. The proof relies on the categorical characterization of the unfolding, and in ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Proceedings ICALP'98, LNCS, pages 296-308. Springer Verlag, 1998.

....proposed as a calculus for owgraphs. Similar considerations arose independently also in di erent contexts, such as the allegories of circuits [3] based on the relational language ruby for circuit design [29] or the languages for (term) graph rewriting [10,11,20] and contextual net processes [22]; or the calculi for concurrent and distributed processes [21,24,28] mostly arising from the work on pre monoidal categories [36] On the other hand, these structures have been used as suitable semantic models, that is, as suitable algebras for modeling the behaviour of dynamic systems, or ....

....structure that could be used as a semantic domain, still retaining suitable properties of freeness. In our opinion, categories of spans [2,7] o er such a domain. Our view is supported by their use as models for circuits and predicate transformers [23,30,31] and as a syntax for nets and graphs [5,10,22]. More generally, it seems to us that these (co)span categories arise naturally in the description of distributed systems with interfaces , lifting and suitably weakening the properties of the underlying categories over which they are built. In the paper we provide a rst analysis of these ....

F. Gadducci and U. Montanari. Axioms for contextual net processes. In K.G. Larsen, S. Skyum, and G. Winskel, editors, Automata, Languages and Programming, volume 1443 of LNCS, pages 296-308. Springer Verlag, 1998.

....sort of data matching. Analogously, codischargers are introduced to represent the explicit creation of data. Several combinations are then possible, where only some of the operators are considered, and their mixed compositions are di erently axiomatized, ranging from the match share categories of [17] to the dgs monoidal categories of [15,16,22] We sketch now a survey of the topic, brie y commenting their role in the literature and the main di erences between similar models. We start with what we call an r monoidal category: One of the various extensions, albeit with a di erent name, ....

.... functor F : C C 0 is a share functor (with respect to r) such that also F op : C op C 0op is so (with respect to op ) We denote by MShCat the category of match share categories (as objects) and match share functors (as arrows) Match share categories have been used in [17] to embed the algebraic properties of processes for contextual nets [31] and, more generally, they can be considered as models for partition based structures. We talk about partitions because, in the set theoretical interpretation, the axioms on the additional operators enforce a sort of ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. Axioms for contextual net processes. In K.G. Larsen, S. Skyum, and G. Winskel, editors, Proc. of ICALP'98, Automata, Languages and Programming, volume 1443 of Lect. Notes in Comp. Science, pages 296-308. Springer Verlag, 1998.

.... have been used to model concurrent accesses to shared data [16] to provide concurrent semantics to concurrent constraint (CC) programs [13] and to model priorities [8] Several concurrent semantics for contextual nets based on processes and event structures have been de ned in the literature [9, 21, 7, 1]. Relying on such concurrent descriptions of contextual net computations, the aim of this paper is to Research partially supported by MURST project Tecniche Formali per Sistemi Software, by TMR Network GETGRATS and by Esprit WG APPLIGRAPH. t0 s t1 t0 t1 t 0 1 # t0 t 00 1 t ....

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Proceedings of ICALP'98, LNCS, pages 296-308. Springer Verlag, 1998.

....of data matching. Analogously, co dischargers are introduced to represent the explicit creation of data. Several combinations are then possible, where only some of the operators are considered, and their mixed compositions are differently axiomatized, ranging from the match share categories of [19] to the dgs monoidal categories of [17,18,24] Here we just sketch a survey of the categorical framework, and briefly comment their role in the literature and the main differences between similar models. We start with what we call a r monoidal category: One of the various extensions, albeit with ....

....a Omega a a ra Fnan Fnan a Fnan Fnan E E E E E E a Omega a Delta a Fnan Fnan a A match share functor F : C Gamma C 0 is a share functor such that also F op is so. We denote by MShCat the category of match share functors. Match share categories have been introduced in [19], and used to embed the algebraic properties of processes for contextual nets [32] They are the basis for a class of categories where suitable models of partition based structures can live. The more interesting axiom of match share categories is depicted in Figure 14. As in match share categories ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Automata, Languages and Programming, volume 1443 of LNCS, pages 296--308. Springer Verlag, 1998.

....of data matching. Analogously, co dischargers are introduced to represent the explicit creation of data. Several combinations are then possible, where only some of the operators are considered, and their mixed compositions are differently axiomatized, ranging from the match share categories of [14] to the dgs monoidal categories of [13, 18] Here we just sketch a survey of the categorical framework, and briefly comment their role in the literature and the main differences between similar models. We start with what we call a r monoidal category: One of the various extensions, albeit with a ....

....a a ra F NaN F NaN a F NaN F NaN E E E E E E a Omega a Delta a F NaN F NaN a A match share functor F : C Gamma C 0 is a share functor such that also F op is so. We denote by MShCat the category of match share functors. Match share categories have been introduced in [14], and used to embed the algebraic properties of processes for contextual nets [25] They are the basis for a class of categories where suitable models of partition based structures can live. Definition 7 (Part Monoidal Categories) A part monoidal category is an 8 tuple hC; Omega ; e; fl; r; ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. Axioms for contextual net processes. In Automata, Languages and Programming, volume 1443 of LNCS, pages 296--308. Springer Verlag, 1998.

No context found.

F. Gadducci and U. Montanari (1998), Axioms for contextual net processes, Proceedings of ICALP 98, K. Larsen et al. (Eds.), Lecture Notes in Computer Science 1443, 296--308, Springer-Verlag.

No context found.

F. Gadducci and U. Montanari (1998), Axioms for contextual net processes, Proceedings of ICALP 98, K. Larsen et al. (Eds.), Lecture Notes in Computer Science 1443, 296--308, Springer-Verlag.

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