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Symbolic Reachability Analysis of Integer Timed Petri Nets

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SOFSEM 2009: Theory and Practice of Computer Science (SOFSEM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5404))

Abstract

Petri nets are an effective formalism to model discrete event systems, and several variants have been defined to explicitly include real time in the model. We consider two fundamental reachability problems for Timed Petri Nets with positive integer firing times: timed reachability (find all markings where the model can be at a given finite time) and earliest reachability (find the minimum time when each reachable marking is entered). For these two problems, we define efficient symbolic algorithms that make use of both ordinary and edge-valued decision diagrams, and provide runtime results on an extensive suite of models.

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References

  1. Bernstein, P.A., Hadzilacos, V., Goodman, N.: Concurrency Control and Recovery in Database Systems. Addison-Wesley, Reading (1987)

    Google Scholar 

  2. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers 35(8), 677–691 (1986)

    Article  MATH  Google Scholar 

  3. Burhard, H.-D.: On priorities of parallelism: Petri nets under the maximum firing strategy. In: Salwicki, A. (ed.) Logic of Programs 1980. LNCS, vol. 148, pp. 86–97. Springer, Heidelberg (1983)

    Chapter  Google Scholar 

  4. Ciardo, G.: Discrete-time Markovian stochastic Petri nets. In: Computations with Markov Chains, pp. 339–358. Kluwer Academic Publishers, Dordrecht (1995)

    Chapter  Google Scholar 

  5. Ciardo, G., Jones, R.L., Miner, A.S., Siminiceanu, R.: Logical and stochastic modeling with SMART. Perf. Eval. 63, 578–608 (2006)

    Article  Google Scholar 

  6. Ciardo, G., et al.: Saturation: An efficient iteration strategy for symbolic state space generation. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 328–342. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Ciardo, G., Marmorstein, R., Siminiceanu, R.: Saturation unbound. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 379–393. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Ciardo, G., Marmorstein, R., Siminiceanu, R.: The saturation algorithm for symbolic state space exploration. STTT 8(1), 4–25 (2006)

    Article  Google Scholar 

  9. Ciardo, G., Siminiceanu, R.: Using edge-valued decision diagrams for symbolic generation of shortest paths. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 256–273. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Ciardo, G., Yu, A.J.: Saturation-based symbolic reachability analysis using conjunctive and disjunctive partitioning. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 146–161. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Dudeney, H.E.: Amusements in Mathematics. Dover (1970)

    Google Scholar 

  12. Holzmann, G.J.: The SPIN Model Checker. Addison-Wesley, Reading (2003)

    Google Scholar 

  13. Jones, N.D., Landweber, L.H., Lien, Y.E.: Complexity of some problems in Petri nets. Theoretical Computer Science 4, 277–299 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kam, T., et al.: Multi-valued decision diagrams: theory and applications. Multiple-Valued Logic 4(1–2), 9–62 (1998)

    MathSciNet  MATH  Google Scholar 

  15. Merlin, P.M.: A study of the recoverability of computing systems. PhD thesis, Department of Information and Computer Science, U. C. Irvine (1974)

    Google Scholar 

  16. Miner, A.S.: Implicit GSPN reachability set generation using decision diagrams. Perf. Eval. 56(1-4), 145–165 (2004)

    Article  Google Scholar 

  17. Murata, T.: Petri nets: properties, analysis and applications. Proc. of the IEEE 77(4), 541–579 (1989)

    Article  Google Scholar 

  18. Pastor, E., Roig, O., Cortadella, J., Badia, R.M.: Petri net analysis using boolean manipulation. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 416–435. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  19. Plateau, B., Fernandes, P., Stewart, W.: The PEPS software tool. In: Kemper, P., Sanders, W.H. (eds.) TOOLS 2003. LNCS, vol. 2794, pp. 98–115. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  20. Zhang, Y.: Non-blocking Synchronization: Algorithms and Performance Evaluation. PhD thesis, Chalmers Univ. of Technology (2003)

    Google Scholar 

  21. Zuberek, W.L.: Timed Petri nets definitions, properties, and applications. Microelectronics and Reliability 31, 627–644 (1991)

    Article  Google Scholar 

  22. Berthomieu, B., Menasche, M.: An enumerative approach for analyzing time Petri nets. In: Proceedings IFIP, pp. 41–46 (1983)

    Google Scholar 

  23. Magnin, M., Molinaro, P., Roux, O.: Decidability, expressivity and state-space computation of stopwatch Petri nets with discrete-time semantics. In: 8th International Workshop on Discrete Event Systems (WODES), pp. 33–38 (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of California, Riverside, USA

    Min Wan & Gianfranco Ciardo

Authors
  1. Min Wan
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  2. Gianfranco Ciardo
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Editor information

Editors and Affiliations

  1. Aarhus Graduate School of Science, University of Aarhus, Ny Munkegade Bldg 1521-110, DK-8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Faculty of Informatics, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Antonín Kučera

  3. Department of Computer Science, University of Aarhus, IT-parken, Aabogade 34, DK-8200, Aarhus N., Denmark

    Peter Bro Miltersen

  4. Ecole Polytechnique, Rue de Saclay, 91128, Palaiseau Cedex, France

    Catuscia Palamidessi  & Frank Valencia  & 

  5. Faculty of Mathematics and Physics, Charles University, Malostranské námestí 25, 118 00, Prague 1, Malá Strana, Czech Republic

    Petr Tůma

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© 2009 Springer-Verlag Berlin Heidelberg

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Wan, M., Ciardo, G. (2009). Symbolic Reachability Analysis of Integer Timed Petri Nets. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science. SOFSEM 2009. Lecture Notes in Computer Science, vol 5404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95891-8_53

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  • DOI: https://doi.org/10.1007/978-3-540-95891-8_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-95890-1

  • Online ISBN: 978-3-540-95891-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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