Abstract
Complementary heuristics are stated to improve the performances of the Farkas algorithm which is used for the computation of a set of generators of positive semi-flows with minimal support in P/T nets. The purpose of this paper concerns a comparative study by means of examples about the performances of these heuristics. It is shown that the heuristics lead sometimes to notable improvements of the Farkas algorithm performance and allow, due to the data structure implemented, the analysis of nets whose size may be arbitrarily large.
These methods have been implemented in a tool called COMBAG which has been developed at Laboratoire de Recherche en Informatique — Bat 490, Université Paris-Sud, F-91405 ORSAY — under the auspices of SYSECA — 315 Bureaux de la Colline, F-92213 St CLOUD.
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H. Alaïwan, J.M. Toudic: "Recherche des semi-flots, des verrous et des trappes dans les réseaux de Petri." TSI vol. 4 no 1, numéro special Réseaux de Petri, G. Memmi (ed.) pp. 103–112 (1985).
G.W. BRAMS: "Réseaux de Petri: théorie et pratique." Masson Ed., Paris (1983).
J. Farkas: "Theorie der einfachen Ungleichungen." In: Journal für die reine und andgewandte Mathematik 124, pp. 1–27 (1902).
J.C. Fiorot, M. Gondran: "Résolution des systèmes linéaires en nombres entiers." Bulletin de la direction des Etudes et Recherches EDF, série C no 2 pp. 65–116
P. Fraisse, C. Johnen, N. Trèves: "SERPE: An Extendable Structure for Analysis of Petri Nets." Proc. of the Advanced Courses on Petri Nets, Bad Honnef, RFA. Rapport interne LRI no 302, Orsay (1986).
H.J. Genrich, K. Lautenbach: "System modelling with high-level Petri Nets" TCS 13, pp. 109–136, North-Holland Pub. co. (1981).
H.J. Genrich, K. Lautenbach: "S-Invariance in Predicate/Transition Nets." In: Applications and Theory of Petri Nets, Pagnoni & Rozenberg ed., Springer-Verlag (1983).
P. Graubman:: "Composition of place transitions nets using additional places and the calculation of their invariants." Internal Report of the Esprit project no 283 FOR-ME-TOO (1985)
S. Haddad, C. Girault: "Algebraic structure of flows of a regular coloured net." Proc. of the 7th European Workshop on Applications and Theory of Petri Nets, Oxford, England (1986).
S. Haddad, JM. Couvreur: "Toward a general and powerful computation of flows in parametrized coloured Petri nets." Proc. IXth European Workshop on Application and Theory of Petri nets, Venice (1988).
T. Hildebrand: "Design and programming of interfaces for monetic applications using Petri nets." In: Advances in Petri nets 84, LNCS vol. 188, G. Rozenberg ed., Springer-Verlag (1985).
K. Jensen: "Coloured Petri Nets and the Invariants Method". TCS 14, pp 317–336, North-Holland Publishing Company (1981).
K. Jensen: "How to find invariants for Coloured Petri Nets." Mathematical Foundations of Computer Science, Vol. 118 pp. 327–338, Gruska and Chytil ed., Springer Verlag (1981).
D.B. Johnson: "Finding all the elementary circuits of a directed graph." SIAM J. Comput, vol 4 no 1 (1975).
F. Krückeberg, M. Jaxy: "Mathematical methods for calculating invariants in Petri Nets." In APN 1987, pp. 106–131, LNCS no 266, Springer-Verlag (1987).
R. Kujansuu, M. Lindqvist: "Efficient algorithms for computing S-Invariants for Predicate/Transition Nets." Proc. of the 5th European Workshop on Applications and Theory of Petri Nets, Aarhus, Denmark (1984).
JL. Lambert: "Consequences of the decidability of the reachability problem for Petri nets." Proc. 8th European Workshop on Application and Theory of Petri nets, pp. 451–470, Zaragoza (1987).
K. Lautenbach, H. Schmid: "Use of Petri nets fo proving correctness of concurrent process systems." Information Processing 1974, pp.187–191, North-Holland Pu. Co. (1974).
J. Martinez, M. Silva: "A simple and fast algorithm to obtain all invariants of a generalized Petri Net." In: C. Girault and W. Reisig ed., Informatik-Fachberichte 52, Springer-Verlag pp. 301–310 (1982).
G. Memmi, G. Roucairol: "Linear algebra in Net Theory." In W. Brauer (ed.): Net Theory and Applications. LNCS 84, Springer-Verlag, Berlin (1980).
G. Memmi: "Méthodes d'analyse des Réseaux de Petri, Réseaux à Files, et applications aux sytèmes Temps-Réel." Thèse de Doctorat d'Etat, Université Pierre et Marie Curie, Paris (1983).
G. Memmi, J. Vautherin: "Analyzing Nets by the Invariant method." In: Advances in Petri Nets 254, pp. 300–336, W. Brauer, W. Reisig, G. Rozenberg (ed.) (1987).
H. Mevissen: "Algebraische Bestimmung von S-Invarianten in Pr/Tr-Netzen." ISF Report, Bonn-GMD (1982).
JL. Peterson: "Petri net theory and the modelling of systems." Prentice Hall (1981).
L. Petrucci, G. Berthelot: "Manuel utilisateur de PETRIX". CNAM Internal Report, to appear, Evry, France (1989).
W. Reisig: "Petri nets with individual tokens". TCS 41 pp. 185–213, North-Holland Pub. co. (1985).
W. Reisig, J. Vautherin: "An algebraic approach to High Level Petri Nets." Proc. 8th Workshop on Application and Theory of Petri Nets, Zaragoza, Spain (1987).
M. Silva, J. Martinez, P. Ladet, H. Alla: "Generalized inverses and the calculation of symbolic invariants for Coloured Petri Nets." TSI vol. 4 no1 numéro special Réseaux de Petri, G. Memmi (ed.) pp. 113–126 (1985).
Y. Souissi, N. Beldiceanu: "Deterministic systems of sequential processes: theory and tools." In: Concurrency 88, pp. 380–400, LNCS, G. Rozenber ed., Springer Verlag (1988).
J.M. Toudic: "Algorithmes d'analyse structurelle des Réseaux de Petri." Thèse de 3è cycle, Université Pierre et Marie Curie (1981).
N. Trèves: "Le calcul d'invariants dans les réseaux de Petri à Prédicats/Transitions Unaires." Thèse de 3è cycle, Université Paris-Sud (1986).
N. Trèves, C. Bagès: "S-CORT, une méthode de conception des systèmes de communication." Proc. Journées Internationales de Génie Logiciel et Applications, pp. 87–104, Toulouse, France (1988).
J. Vautherin, G. Memmi: "Computation of flows for Unary-Predicate/Transition nets." In: Advances in Petri Nets 1984, LNCS 188, G. Rozenberg ed. pp. 455–467, Springer-Verlag (1985).
J. Vautherin: "Calculation of semi-flows of Pr/T-systems." Proc. of International Workshop on Petri Nets and Performance models, Madison, Winconsin, USA (1987).
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Treves, N. (1990). A comparative study of different techniques for semi-flows computation in place/transition nets. In: Rozenberg, G. (eds) Advances in Petri Nets 1989. APN 1988. Lecture Notes in Computer Science, vol 424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52494-0_40
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DOI: https://doi.org/10.1007/3-540-52494-0_40
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