V. SASSONE (1994), On the Semantics of Petri Nets: Processes, Unfoldings, and Infinite Computations.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....commutativity (up to equivalence) of a diagram analogous to the one above involving all the configurations of EFU[N ] and the comma category hu N #DP[N ] i. Unfortunately, due to lack of space, we shall not say more about this extension here. The details of this construction can be found in [22]. Concerning the organization of the paper, in Section 1 we recall the basic facts about the algebraic approach to Petri nets as given in [11] and [6] Then, in Section 2 we give a brief overview of the formal development concerning the unfolding semantics introduced in [12] In Section 3 we ....

.... we study the decorated concatenable processes of N and their axiomatization as the arrows of the symmetric monoidal category DP[N ] Due to the extended abstract nature of this paper, we omit all proofs; the interested reader is referred to [14] Some of the results presented here appear also in [22]. 1 Petri Nets and their Processes In this section we briefly recall the basic definitions about Petri nets (see [21] for a thorough introduction) and their processes. Notation. Throughout the paper, S Phi denotes the set of finite multisets on the set S. We recall that S Phi is a ....

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V. Sassone. On the Semantics of Petri Nets: Processes, Unfoldings, and Infinite Computations. PhD Thesis, TD 6/94 Dipartimento di Informatica, Universit`a di Pisa, March 1994.

.... to avoid this approach because on the one hand it would not give any further real insight into the subject, whilst, on the other hand, it would still leave unresolved the key issue of functoriality for DP [ and P[ Further research is currently ongoing on these open questions, e.g. [29, 27]. Although DP [ is defined only at the object level, we think that the paper presents interesting results, providing a natural and unified account of the algebraic, the process oriented, and the denotational views of net semantics. It is worth remarking once again that the notion underlying ....

....Then, one can prove the commutativity (up to equivalence) of a diagram analogous to the one above involving all the configurations of EFU [N ] and the comma category #uN #DP [N ] # #. However, we shall not say more about this extension here; the details of the construction can be found in [27]. Concerning the organization of the paper, in Section 1 we recall the basic facts about the algebraic approach to Petri nets as given in [14] and [6] Then, in Section 2 we give a brief overview of the formal development concerning the unfolding semantics introduced in [15] In Section 3 we ....

[Article contains additional citation context not shown here]

V. Sassone. On the Semantics of Petri Nets: Processes, Unfoldings, and Infinite Computations. PhD Thesis, Dipartimento di Informatica, Universita di Pisa, 1994.

....to discover and amend a significant anomaly of concatenable processes which, although of general relevance, would have not been easily noticed in other frameworks. This paper is a full and extended version of (Sassone 1995) Some preliminary related results appear also in the author s thesis (Sassone 1994). Notation. Given a category C, we denote the composition of arrows in C by the usual symbol ffi and follow the usual right to left order. The identity of c 2 C is written as id c . However, we make the following exception. When dealing with a category in which arrows are meant to represent ....

....speaking, the problem is that the category of symmetries sitting inside P (N) say Sym N , is not free on N. Clearly, this is due to first axiom of Definition 1.5, a conditional axiom with a negative premise. To make things worse, the theory illustrated extensively in (Degano et al. 1996; Sassone 1994) makes it clear that, in order for P (N) to maintain its interesting computational meaning, such an axiom is strictly needed. Moreover, it is easy to verify that as soon as one imposes further axioms on P (N) which guarantee to get a functor, one annihilates all the symmetries and, therefore, ....

V. SASSONE (1994), On the Semantics of Petri Nets: Processes, Unfoldings, and Infinite Computations.

....framework made it possible to discover and amend an anomaly of P [ significant and of general relevance which could have not been noticed in other frameworks. Due to the extended abstract nature of this paper, most of the proofs are omitted. Some preliminary related results appear also in [11]. Notation. When dealing with a category C in which arrows are meant to represent computations, in order to stress its computational interpretation, we write arrow composition from left to right, i.e. in the diagrammatic order, and we denote it by ; The reader is referred to [5] for the ....

V. Sassone. On the Semantics of Petri Nets: Processes, Unfoldings, and Infinite Computations. PhD Thesis TD 6/94, Dipartimento di Informatica, Universit`a di Pisa, 1994.

....[N] w are possibly infinite decorated concatenable processes. Then, one can prove the commutativity (up to equivalence) of a diagram analogous to the one above involving all the configurations of EFU[N] and the comma category hu N #DP [N] w i. The details of this construction can be found in (Sassone 1994). On the Semantics of Petri Nets 35 ....

Sassone, V. (1994) On the Semantics of Petri Nets: Processes, Unfoldings, and Infinite Computations. PhD Thesis, TD 6/94 Dipartimento di Informatica, Universita di Pisa, Italy.

....it possible to discover and amend a significant anomaly of P[ which, although of general relevance, would have not been easily noticed in other frameworks. Due to the extended abstract nature of this exposition, most of the proofs are omitted. Some preliminary related results appear also in [11]. Notation. When dealing with a category C in which arrows are meant to represent computations, in order to stress their computational interpretation, we write arrow composition from left to right, i.e. in the diagrammatic order, and we denote it by ; The reader is referred to [5] for the ....

V. Sassone. On the Semantics of Petri Nets: Processes, Unfoldings, and Infinite Computations. PhD Thesis TD 6/94, Dipartimento di Informatica, Universit`a di Pisa, 1994.

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