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On weighted T-systems

  • E. Teruel
  • P. Chrzastowski-Wachtel
  • J. M. Colom
  • M. Silva
Submitted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 616)

Abstract

Structure theory is a branch of net theory devoted to investigate the relationship between the structure and the behaviour of net system models. Many of its powerful results have been derived for some subclasses of ordinary net systems. The aim of this contribution is to draw a general perspective of the structure theory for a subclass with Marked Graph-like underlying graph but allowing weights: weighted T-graphs (WTG). Weights are convenient to properly model systems with bulk services and arrivals. Properties of WTG and the corresponding weighted T-systems (WTS) are presented at three different levels: purely structural (e.g. in consistent WTG conservativeness is equivalent to strong connectedness), inter-relationships between the structure and the behaviour (e.g. structural liveness and boundedness is equivalent to consistency and strong connectedness) and liveness and reachability characterizations (e.g. deciding liveness is linear wrt. the 1-norm of the unique minimal T-semiflow of a consistent, even unbounded, WTS). Classical results for Marked Graphs can be derived as corollaries. Nevertheless, even in live and consistent WTS, important properties of Marked Graphs do not hold (e.g. P-semiflows based characterization of reachability).

Keywords

Structure theory weighted T-graphs Marked Graphs 

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References

  1. [Brams 83]
    G.W. Brams. Réseaux de Petri: Théorie et Pratique. Masson. Paris, 1983.Google Scholar
  2. [Brauer 42]
    A. Brauer. On a problem of partitions. Amer.J.Math., 64. 1942.Google Scholar
  3. [CCCS 92]
    J. Campos, G. Chiola, J.M. Colom, M. Silva. Properties and Performance Bounds for Timed Marked Graphs. IEEE Transactions on Circuits and Systems, vol.39, no.5. May, 1992.Google Scholar
  4. [CCS 90]
    J.M. Colom, J. Campos, M. Silva. On Liveness Analysis Through Linear Algebraic Techniques. In Deliverables Covering the Period June 1989 to June 1990, Esprit Basic Research Action 3148 (DEMON), W.G.6. Paris, France. June, 1990.Google Scholar
  5. [CHEP 71]
    F. Commoner, A.W. Holt, S. Even, A. Pnueli. Marked Directed Graphs. J. Comput. System Sci., 5. 1971.Google Scholar
  6. [Colom 89]
    J.M. Colom. Análisis Estructural de Redes de Petri. Programación Lineal y Geometría Convexa. PhD Thesis, Dpto. Ing. Eléctrica e Informática, Universidad de Zaragoza. June, 1989.Google Scholar
  7. [CS 91]
    J.M. Colom, M. Silva. Improving the linearly based characterization of P/T nets. In APN 90, LNCS vol. 483. Springer-Verlag. Berlin, 1991.Google Scholar
  8. [Deo 74]
    N. Deo: Graph Theory with Applications to Engineering and Computer Science. Prentice-Hall, Inc. Englewood Cliffs, N.J., 1974.Google Scholar
  9. [GL 73]
    H.J. Genrich, K. Lautenbach. Synchronisationsgraphen. Acta Informatica, 2. 1973.Google Scholar
  10. [HL 65]
    B.R. Heap, M.S. Lynn. On a Linear Diophantine Problem of Frobenius: an Improved Algorithm. Numer.Mat., 7. 1965.Google Scholar
  11. [KM 69]
    R.M. Karp, R.E. Miller. Parallel Program Schemata. J. Comput. System Sci., 3. 1969.Google Scholar
  12. [Lien 76]
    Y.H. Lien. Termination Properties of Generalized Petri Nets. Siam J. Comput., vol.5, no.2. June, 1976.Google Scholar
  13. [LR 78]
    L.H. Landweber, E.L. Robertson. Properties of Conflict-Free and Persistent Petri Nets. J. ACM, vol.25, no.3. July, 1978.Google Scholar
  14. [Murata 77]
    T. Murata. Circuit Theoretic Analysis and Synthesis of Marked Graphs. IEEE Trans. on Circuits and Systems, vol.CAS-S4,no.7. July,1977.Google Scholar
  15. [Murata 89]
    T. Murata. Petri Nets: Properties, Analysis and Applications. Procs. IEEE, vol.77, no.4. April, 1989.Google Scholar
  16. [Murty 83]
    K.G. Murty. Linear Programming. Wiley and Sons. New York, 1985.Google Scholar
  17. [SC 88]
    M. Silva, J.M. Colom. On the Computation of Structural Synchronic Invariants in P/T Nets. In APN 88, LNCS vol.340. Springer-Verlag. Berlin, 1988.Google Scholar
  18. [Silva 85]
    M. Silva. Las Redes de Petri: en la Automática y la Informática. AC. Madrid, 1985.Google Scholar
  19. [Souissi 90]
    M.Y. Souissi. Une étude de la préservation de propriétes par composition de réseaux de Pétri. Quelques extensions aux réseaux à files. Application à la validation de protocoles de communication. PhD Thesis, Université Pierre et Marie Curie. February, 1990.Google Scholar
  20. [TCCS 92]
    E. Teruel, P. Chrzastowski-Wachtel, J.M. Colom, M. Silva. On Weighted T-Systems. Research Report GISI-RR-92-04. Dpto. Ing. Eléctrica e Informática, Universidad de Zaragoza. January, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • E. Teruel
    • 1
  • P. Chrzastowski-Wachtel
    • 2
  • J. M. Colom
    • 1
  • M. Silva
    • 1
  1. 1.Dpto. Ing. Eléctrica e InformáticaUniversidad de ZaragozaZaragozaSpain
  2. 2.Institute of InformaticsWarsaw UniversityWarszawaPoland

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