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Timed Petri nets and temporal linear logic

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Application and Theory of Petri Nets 1997 (ICATPN 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1248))

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Abstract

It is well known that Petri nets constitute the algebraic structure of quantales, which can be models of linear logic. As a timed extension to quantales, timed R-monoids are defined, which are constructed from timed Petri nets. Next, temporal linear logic is introduced, which has timed Petri nets as its models, i.e., whose formulas can be interpreted as sets of timed markings of a timed Petri net. Soundness of the logic with respect to timed Petri net interpretation is shown. Finally, examples show how to express properties of timed Petri nets by temporal linear logic.

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References

  1. J. V. Benthem. The Logics of Time, chapter I. Kluwer Academic Publishers, 2nd edition, 1991.

    Google Scholar 

  2. I. I. Bestuzheva and V. V. Rudnev. Timed Petri nets: Classification and comparative analysis. Automation and Remote Control, 51(10):1308–1318, Oct 1990.

    Google Scholar 

  3. C. Brown. Petri nets as quantales. Technical Report ECS-LFCS-89-96, Department of Computer Science, University of Edinburgh, November 1989.

    Google Scholar 

  4. C. Brown. Temporal logic and categories of Petri nets. In Automata, Languages and Programming, LNCS 700, pages 570–581, 1993.

    Google Scholar 

  5. M. Diaz and P. Senac. Time stream Petri nets: a model for timed multimedia information. In Application and Theory of Petri Nets, LNCS 815, pages 219–238, 1994.

    Google Scholar 

  6. M. Diaz. Design of multimedia protocols. In Multimedia Modeling '95, pages 35–50. IEEE, World Scientific, 1995.

    Google Scholar 

  7. R. Durchholz. Causality, time, and deadlines. Data & Knowledge Engineering, 6:459–477, 1991.

    Google Scholar 

  8. U. Engberg and G. Winskel. Linear logic on Petri nets. In A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium, LNCS 803, pages 176–229, Jun 1993.

    Google Scholar 

  9. F. Fabre and P. Senac. A toolkit for the modelling of multimedia synchronization scenarios. In Multimedia Modeling '95, pages 187–201. IEEE, World Scientific, 1995.

    Google Scholar 

  10. M. Felder, C. Ghezzi, and M. Pezzé. Analyzing refinements of state based specifications: the case of TB nets. In International Symposium on Software Testing and Analysis, Boston, June 1993.

    Google Scholar 

  11. M. Felder and A. Morzenti. A temporal logic approach to implementation and refinement in timed Petri nets. In First International Conference, ICTL '94, LNCS 827, pages 365–381, 1994.

    Google Scholar 

  12. F. Panzieri and R. Davoli Date. Real time systems: A tutorial. Technical Report UBLCS-93-22, University of Bologna, October 1993.

    Google Scholar 

  13. J. Gallier. Constructive logics. part II: Linear logic and proof nets. Research report, Degital Equipment Corporation, 1991.

    Google Scholar 

  14. C. Ghezzi, D. Mandrioli, S. Morasca, and P. Mauro. A general way to put time into Petri nets. In Proceedings of the Fifth International Workshop on Software Specification, volume 14-3 of ACM SIGSOFT Engineering Notes, pages 60–67. Pittsburgh, Pennsylvania, USA, May 1989.

    Google Scholar 

  15. C. Ghezzi, S. Morasca, and P. Mauro. Validating timing requirements for TB net specifications. 1994.

    Google Scholar 

  16. J. Y. Girard. Linear logic. Theoretical Computer Science, 50:1–102, 1987.

    Article  Google Scholar 

  17. R. Goldbratt. Logics of The Time and Computation. Number 7 in Lecture Notes. Center for The Study of Language and Information.

    Google Scholar 

  18. H. M. Hanisch. Analysis of place/transition nets with timed arcs and its application to batch process control. In Application and Theory of Petri Nets, number 691 in LNCS, pages 282–299, 1993.

    Google Scholar 

  19. R. Howell. A taxonomy of fairness and temporal logic problems for Petri nets. Theoretical Computer Science, 82:341–372, 1991.

    Google Scholar 

  20. J. Carlier and P. Chretienne. Timed Petri net schedules. In Advances in Petri Nets, number 340 in LNCS, pages 62–84, 1988.

    Google Scholar 

  21. M. Kanovich. Petri nets, Horn programs, linear logic, and vector games. In Theoretical Adpects of Computer Software, International Symposium, LNCS 789, pages 642–666, 1994.

    Google Scholar 

  22. N. Kawakatsu, R. Nakajima and M. Tanabe. RSM: Real-time synchronization machines for continuous media presentation. In International Conference on Virtual Systems and Multimedia '96 in Gifu (Japan), volume 2nd, November 1996.

    Google Scholar 

  23. J. Lilius. High-level nets and linear logic. In K. Jensen, editor, Application and Theory of Petri Nets 1992, 13th International Conference, LNCS 616, pages 310–327, Sheffield, UK, June 1992.

    Google Scholar 

  24. J. Meseguer and U. Montanari. Petri nets are monoids. INFORMATION AND COMPUTATION, 88:105–155, 1990.

    Article  Google Scholar 

  25. W. Reisig. Petri Nets: an Introduction. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1985.

    Google Scholar 

  26. P. Senac, P. Sannes, and R. Willrich. Hierarchical time stream Petri net: a model for hypermedia systems. In Application and Theory of Petri Nets, LNCS 935, pages 451–470, 1995.

    Google Scholar 

  27. M. Tanabe and R. Nakajima A logical basis for continuous-media presentation with QoS. In Multimedia Modeling '95, the 2nd International Conference of Multimedia Modeling. IEEE, World Scientific, 1995.

    Google Scholar 

  28. M. Woo, N. U. Qazi, and A. Ghafoor. A synchronization framework for communication of pre-orchestrated multimedia information. IEEE Network, pages 52–61, January/February 1994.

    Google Scholar 

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Japan

    Makoto Tanabe

Authors
  1. Makoto Tanabe
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Pierre Azéma Gianfranco Balbo

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© 1997 Springer-Verlag Berlin Heidelberg

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Tanabe, M. (1997). Timed Petri nets and temporal linear logic. In: Azéma, P., Balbo, G. (eds) Application and Theory of Petri Nets 1997. ICATPN 1997. Lecture Notes in Computer Science, vol 1248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63139-9_35

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  • DOI: https://doi.org/10.1007/3-540-63139-9_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63139-2

  • Online ISBN: 978-3-540-69187-7

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