Abstract
The aim of this paper is the study of semantics, compositionality and net properties (as quasi-liveness of transitions, boundedness of places, termination of nets, deadlocks, coverness) of algebraic high-level nets in a categorical framework. We show that the algebraic high-level nets can be composed in a elegant manner using colimits and especially pushouts. We define two kinds of semantics for algebraic high-level nets: the standard semantics and normed scheme semantics, prove that both semantics are compositional, and study in which way the above net properties can be analyzed.
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6. Bibliography
G. Berthelot, C. Johnen, L.Petrucci: PAPETRI: Poste d'Analyse des réseaux de PETRI. Rapport de Recherche LRI 527, Université de Paris-Sud, 1989.
G. Berthelot, L. Petrucci: Putting algebraic nets into practice. Internal report CEDRIC-IIE, 1989.
C. Dimitrovici, U. Hummert: Semantische Konstruktionen und Kategorien algebraischer Netzschemata. Technische Report 12, TU Berlin 1989.
C. Dimitrovici, U. Hummert: Kategorielle Konstruktionen für algebraische Petrinetze. Technische Report 23, TU Berlin 1989.
H. Ehrig, A. Heise, U. Hummert: Algebraic High-Level Nets with Capacities. Technische Report, TU Berlin 1989.
H. Ehrig, B. Mahr: Fundamentals of Algebraic Specifications 1. Springer Verlag, 1985.
H. Ehrig, B. Mahr: Fundamentals of Algebraic Specifications 2. Springer Verlag, 1990.
U. Hummert: High-Level-Netze. Technische Report 10, TU Berlin 1987.
U. Hummert: Algebraische Theorie von High-Level-Netzen. Doktorarbeit, TU Berlin 1989.
K. Jensen: Colored Petri Nets and the Invariant Method. TCS 14, 1981, pp. 317–336.
K. Jensen: Colored Petri Nets. Advances in Petri Nets 1986, LNCS 254, 1987, pp. 248–299.
S. MacLane: Categories for the Working Mathematician. Springer Verlag, 1971.
J. Meseguer, U. Montanari: Petri Nets Are Monoids. Stanford Research Institute, Report SRI CSL-88-3, 1988.
G. Memmi, J. Vautherin: Analysing Petri Nets by the Invariant Method. Rapport de Recherche LRI 319, Université de Paris-Sud, 1986.
W. Reisig: Petri Nets. Springer Verlag, 1985.
W. Reisig: Petri Nets with Individual Tokens. TCS 41, 1985, pp. 185–213.
J. Vautherin: Un modèle algébrique, basé sur les réseaux de Petri, pour l'étude des systèmes parallèles. Thèse de doctorat d'ingénieur, Université de Paris-Sud, 1985.
J. Vautherin: Parallel Systems Specifications with Colored Petri Nets and Algebraic Specifications. Advances in Petri Nets 1987, LNCS 266, p. 293–308.
G. Winskel: Petri Nets, Algebras, Morphisms, and Compositionality. Inf. and Comp. 72, 1987.
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© 1991 Springer-Verlag Berlin Heidelberg
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Dimitrovici, C., Hummert, U., Petrucci, L. (1991). Semantics, composition and net properties of algebraic high-level nets. In: Rozenberg, G. (eds) Advances in Petri Nets 1991. ICATPN 1990. Lecture Notes in Computer Science, vol 524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019971
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DOI: https://doi.org/10.1007/BFb0019971
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