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Analysing Nets by the Invariant Method

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Petri Nets: Central Models and Their Properties (ACPN 1986)

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Abstract

Methods for analysing P/T-systems can be roughly divided into several categories: study of the reachability set, transformation by homomorphism, and invariants. Each of these methods have advantages and disadvantages.

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Bibliography

  1. Groupe ADJ: J. A. Goguen, J. W. Thatcher and E. G. Wagner “An initial algebra approach to the specification, correctness and implementation of abstract data types” Current Trends in Programming Methodology, Vol. IV, R. T. Yeh (Ed.), Prentice Hall, New Jersey (1978).

    Google Scholar 

  2. H. Alaiwan and J. M. Toudic “Recherche des semi-flows, des verrous et des trappes dans les réseaux de Petri”. T. S. I., Vol,4, N°1-Numero spécial réseaux de Pétri, G. Memmi (Ed.), pp 103-112 (1985).

    Google Scholar 

  3. P. Behm and G. Memmi “Rafael: Un outil d’analyse de systèmes temps réel”. 2ème Colloque de Génie Logiciel AFCET, Nice, pp 13-32 (1984).

    Google Scholar 

  4. F. Boussinot “Réseaux de processus avec mélange équitable: une approche du temps réél”. Thèse d’état, Université Paris VII (1981).

    Google Scholar 

  5. F. Boussinot, R. Martin, G. Memmi, G. Ruggiu and J. Vapné “A language for formal descriptions of real time systems”. Proc. of SAFECOMP’83 — 3rd IFAC/IFIP Workshop, J. A. Baylis (Ed.), Pergamon Press, Cambridge UK. (1983).

    Google Scholar 

  6. G. W. Brams “Réseaux de Pétri: théorie et pratique”. Tome 1, Edition Masson, Paris (1982).

    Google Scholar 

  7. H. Ehrig and B. Mahr “Fundamentals of Algebraic Specification 1: Equations and Initial Semantics”. EATCS Monographs on Theoretical Computer Science, Vol. 6, W. Brauer, G. Rozenberg, A. Salomaa (Eds.), Springer Verlag (1985)

    Google Scholar 

  8. J. Farkas “Theorie der einfachen Ungleichungen”. Journal für reine und angew. Mathematik 124, pp 1–27 (1902).

    Google Scholar 

  9. M. C. Gaudel “Algebraic Specification of Abstract Data Type”. R. R. N° 360, INRIA, Le Chesnay (1979).

    Google Scholar 

  10. P. Graubmann “Composition of place transition nets using additional places (or transitions) and the calculation of their invariants”. Internal Report of the Esprit project n° 283 FO-ME-TOO, September 1985 (1985).

    Google Scholar 

  11. S. Haddad and C. Girault “Algebraic structure of flows of a regular coloured net”. 7th European Workshop on Application and Theory of Petri Nets, Oxford, June 1986 (1986).

    Google Scholar 

  12. P. Huber, A. M. Jensen, L. O. Jepsen and K. Jensen “Towards reachability trees for high-level Petri nets”, in “Advances in Petri Nets 1984”, L. N. C. S. 188, G. Rozenberg (Ed.), Springer Verlag, pp 215-233. (1985).

    Google Scholar 

  13. K. Lautenbach and H. Schmid “Use of Petri nets for proving correctness of concurrent process systems”. Information Processing 1974 — North Holland Pub. Co., pp 187-191 (1974).

    Google Scholar 

  14. K. Jensen “Coloured Petri nets and the invariant method”. T. C. S. 14, pp 317–336 (1981).

    Article  MATH  Google Scholar 

  15. J. Martinez and M. Silva “A simple and fast algorithm to abtain all invariants of a generalized Petri Net“. Informatik — Fachbrichte 52, C. Girault and W. Reisig (Eds.), Springer Verlag, pp 301-310, (1982).

    Google Scholar 

  16. P. Mateti and D. Nardingh “On algorithms for enumerating all circuits of a graph”. SIAM J. Comput., Vol. 5, N°1, pp 90–99 (1976).

    Article  MathSciNet  Google Scholar 

  17. G. Memmi and G. Roucairol “Linear algebra in net theory”. Proc. of “Advanced Course on genral Net Theory of Processes and Systems” Hambourg 1979, L. N. C. S. 84, W. Brauer (Ed.), Springer Verlag (1980).

    Google Scholar 

  18. G. Memmi “Contrôle du parallélisme et détection des blocages”. Journée de Synthèse “Quelques outils d’aideà la conception et à la réalisation de systèmes informfatiques”. AFCET — Informatique Gif/s/Yvette, pp 35-69, (1981).

    Google Scholar 

  19. G. Memmi “Methode d’analyse de réseaux de Petri, réseaux à files, et applications aux systèmes temps réel”. Thèse de Doctorat d’Etat, Université Pierre et Marie Curie, Juin 1983 (1983)

    Google Scholar 

  20. G. Memmi and A. Finkel “An introduction to fifo nets — monogeneous nets: a subclass of fifo nets”. T. C. S. 35, pp 191–214, (1985).

    Article  MathSciNet  MATH  Google Scholar 

  21. M. Silva, J. Martinez, P. Ladet and H. Alla “Generalized inverses and the calculation of symbolic invariants for coloured Petri nets”. T. S. I., Vol. 4, N°1 — Numéro spécial Réseaux de Petri, G. Memmi (Ed.), pp 113-126, (1985).

    Google Scholar 

  22. J. M. Toudic “Algorithmes d’analyse structurelle des réseaux Petri“. Thèse de 3ème cycle, Université Pierre et Marie Curie, Octobre 1981 (1981).

    Google Scholar 

  23. J. Vautherin “Un modèle algébrique, basé sur les réseaux de Petri, pour l’étude des systèmes parallèles”. Thèse de Docteur-Ingénieur, Université Paris-Sud, Juin 1985 (1985).

    Google Scholar 

  24. J. Vautherin and G. Memmi “Computation of flows for unary Predicates/Transitions nets”, in “Advances in Petri Nets 1984”, L. N. C. S. 188, G. Rozenberg (Ed.), Springer Verlag, pp 307-327 (1985).

    Google Scholar 

  25. J. Vautherin “Parallel systems specifications with coloured Petri nets and algebraic abstract data types”. 7th European Workshop on Application and Theory of Petri Nets, Oxford, June 1986 (1986).

    Google Scholar 

  26. J. Vautherin “Calculation of semi-flows of Pr/T-systems”. Research Report L. R. I., N° 130, Université Paris Sud, Octobre 1986 (1986).

    Google Scholar 

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© 1987 Springer-Verlag Berlin Heidelberg

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Memmi, G., Vautherin, J. (1987). Analysing Nets by the Invariant Method. In: Brauer, W., Reisig, W., Rozenberg, G. (eds) Petri Nets: Central Models and Their Properties. ACPN 1986. Lecture Notes in Computer Science, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47919-2_11

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  • DOI: https://doi.org/10.1007/978-3-540-47919-2_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17905-4

  • Online ISBN: 978-3-540-47919-2

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