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Abstract: . The concatenable processes of a Petri net N can be characterized abstractly as the arrows of a symmetric monoidal category P[N ]. Yet, this is only a partial axiomatization, since P[N ] is built on a concrete, ad hoc chosen, category of symmetries. In this paper we give a fully equational description of the category of concatenable processes of N , thus yielding an axiomatic theory of the noninterleaving behaviour of Petri nets. Introduction C oncatenable processes of Petri nets have... (Update)
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.... domain (or, equivalently, a prime event structure) models the computations of a safe net [9] The research detailed in [6, 3, 4, 14, 7, 8, 16] identifies such structures as symmetric monoidal categories where objects are states, i.e. multisets of tokens, arrows are...
...recall this construction. The axiomatization of P[N ] presented here has been proved to be equivalent to the original formulation in [28]. Recall that a symmetric strict monoidal category (see [12] for a thorough elementary introduction) is a category C together with a...
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0.5: An Approach to the Category of Net Computations - Sassone (Correct)
0.3: The Algebraic Structure of Petri Nets - Sassone (2000) (Correct)
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BibTeX entry: (Update)
V. SASSONE (1995), Axiomatizing Petri Net Concatenable Processes, in Proceedings of FCT'95, H. Reichel (Ed.), LNCS n. 965, Springer-Verlag, 414--423. http://citeseer.ist.psu.edu/sassone95axiomatizing.html More
@inproceedings{ sassone95axiomatizing,
author = "Vladimiro Sassone",
title = "Axiomatizing Petri Net Concatenable Processes",
booktitle = "Fundamentals of Computation Theory",
pages = "414-423",
year = "1995",
url = "citeseer.ist.psu.edu/sassone95axiomatizing.html" }
Citations (may not include all citations):236 Categories for the Working Mathematician (context) - MacLane
113 Functorial Semantics of Algebraic Theories (context) - Lawvere - 1963
97 Information and Computation (context) - Meseguer, Montanari et al.
59 The Non-Sequential Behaviour of Petri Nets (context) - Goltz, Reisig
55 Sequential and Concurrent Behaviour in Petri Net Theory (context) - Best, Devillers
39 Closed Categories (context) - Eilenberg, Kelly
32 Axiomatizing Net Computations and Processes (context) - Degano, Meseguer et al.
17 On MacLane's Conditions for Coherence of Natural Associativi.. (context) - Kelly
13 Natural Associativity and Commutativity (context) - MacLane
10 Concerning the abstract group of order k (context) - Moore
10 Gesellschaft fur Mathematik und Datenverarbeitung (context) - Petri, Interner et al.
9 Scone: A Simple Calculus of Nets (context) - Gorrieri, Montanari
8 Dipartimento di Informatica (context) - Sassone, Semantics et al.
3 Some Remarks on Concatenable Processes (context) - Sassone
2 Bulletin American Mathematical Society (context) - MacLane
1 Comptes Rendus Academie Science Paris (context) - enabou, Multiplication
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