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.
A part of this work was granted by the Esprit project FOR-ME-TOO.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
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).
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).
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).
F. Boussinot “Réseaux de processus avec mélange équitable: une approche du temps réél”. Thèse d’état, Université Paris VII (1981).
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).
G. W. Brams “Réseaux de Pétri: théorie et pratique”. Tome 1, Edition Masson, Paris (1982).
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)
J. Farkas “Theorie der einfachen Ungleichungen”. Journal für reine und angew. Mathematik 124, pp 1–27 (1902).
M. C. Gaudel “Algebraic Specification of Abstract Data Type”. R. R. N° 360, INRIA, Le Chesnay (1979).
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).
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).
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).
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).
K. Jensen “Coloured Petri nets and the invariant method”. T. C. S. 14, pp 317–336 (1981).
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).
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).
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).
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).
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)
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).
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).
J. M. Toudic “Algorithmes d’analyse structurelle des réseaux Petri“. Thèse de 3ème cycle, Université Pierre et Marie Curie, Octobre 1981 (1981).
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).
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).
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).
J. Vautherin “Calculation of semi-flows of Pr/T-systems”. Research Report L. R. I., N° 130, Université Paris Sud, Octobre 1986 (1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Springer Book Archive