Advertisement

On Computation Complexity of the Concurrently Enabled Transition Set Problem

  • Li Pan
  • Weidong Zhao
  • Zhicheng Wang
  • Gang Wei
  • Shumei Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)

Abstract

In this paper, we propose a new decision problem, called the concurrently enabled transition set problem, which is proved to be NP-complete by reduction from the independent set problem. Then, we present a polynomial-time algorithm for the maximal concurrently enabled transition set problem, and prove that some special subproblems are in P by the proposed algorithm.

Keywords

Polynomial Time Decision Problem Deterministic Algorithm Input Place Step Execution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Murata, T.: Petri nets, properties, analysis and applications. Proc. IEEE 77(4), 541–580 (1989)CrossRefGoogle Scholar
  2. 2.
    Girault, C., Valk, R.: Petri Nets for Systems Engineering. A Guide to Modeling, Verification, and Applications. Springer, Heidelberg (2003)Google Scholar
  3. 3.
    Jeffrey, J., Lobo, J., Murata, T.: A High-Level Petri Net for Goal-Directed Semantics of Horn Clause Logic. IEEE Transactions on Knowledge and Data Engineering 8(2), 241–259 (1996)CrossRefGoogle Scholar
  4. 4.
    Mukund, M.: Petri Nets and Step Transition Systems. International Journal of Foundations of Computer Science 3(4), 443–478 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Jucan, T., Vidraşcu, C.: Concurrency-degrees for Petri nets. In: Proc. of the 1st Conference on Theoretical Computer Science and Informatics Technologies - CITTI 2000, Ovidius University of Constanta, Romania, May 25-27, 2000, pp. 108–114 (2000)Google Scholar
  6. 6.
    Vernadat, F., Azéma, P., Michel, F.: Covering step graph. In: Billington, J., Reisig, W. (eds.) ICATPN 1996. LNCS, vol. 1091, pp. 516–535. Springer, Heidelberg (1996)Google Scholar
  7. 7.
    Ribet, P.O., Vernadat, F., Berthomieu, B.: On combining the persistent sets method with the covering steps graph method. In: Peled, D.A., Vardi, M.Y. (eds.) FORTE 2002. LNCS, vol. 2529, pp. 344–359. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Pan, L., Chen, D., Li, W.: Reachability Analysis of Time-Independent Choice TPN. In: 10th Joint International Computer Conference, Kunming, China, Novermber 2004, pp. 629–634 (2004)Google Scholar
  9. 9.
    Cheng, A., Esparza, J., Palsberg, J.: Complexity Results for 1-safe Nets. Theoret. Comput. Sci. 147, 117–136 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Esparza, J.: Reachability in live and safe free-choice Petri nets is NP-complete. Theoretical Computer Science 198(1-2), 211–224 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Stewart, I.A.: On the reachablility problem for some classes of Petri nets. Research Report, University of Newcastle upon Tyne (1992)Google Scholar
  12. 12.
    Howell, R., Rosier, L.: Completeness results for conflict-free vector replacement system. Journal of Computer and System Sciences 37, 349–366 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Howell, R., Rosier, L., Yen, H.: Normal and Sinkless Petri Nets. Journal of Computer and System Sciences 46, 1–26 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Watanabe, T., et al.: Time complexity of legal firing sequences and related problems of Petri nets. Trans. IEICE of Japan 72(12), 1400–1409 (1989)Google Scholar
  15. 15.
    Watanabe, T., Mizobata, Y., Onaga, K.: Legal firing sequences and minimum initial markings for Petri nets. In: IEEE International Symposium on Circuits and Systems, vol. 1, pp. 323–326 (1989)Google Scholar
  16. 16.
    Badouel, E., Bernardinello, L., Darondeau, P.: The synthesis problem for elementary net systems is NP-complete. Theoretical Computer Science 186, 107–134 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Esparza, J.: Decidability and complexity of Petri net problems - an introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998)Google Scholar
  18. 18.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)zbMATHGoogle Scholar
  19. 19.
    Paradimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Li Pan
    • 1
  • Weidong Zhao
    • 1
  • Zhicheng Wang
    • 1
  • Gang Wei
    • 1
  • Shumei Wang
    • 1
  1. 1.Tongji University, Shanghai 200092, CAD Research CenterChina

Personalised recommendations