Skip to main content
SpringerLink
Log in
Book cover

International Conference on Application and Theory of Petri Nets

ICATPN 1993: Application and Theory of Petri Nets 1993 pp 513–531Cite as

A unified approach for reasoning about conflict-free Petri nets

  • Full Papers
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 691))

Abstract

The aim of this paper is to develop a unified approach for deriving complexity results for problems concerning conflict-free Petri nets. To do so, we first define a class of formulas for paths in Petri nets. We then show that answering the satisfiability problem for conflictfree Petri nets is tantamount to solving a system of linear inequalities (which is known to be in P). Since a wide spectrum of Petri net problems (including various fairness-related problems) can be reduced to the satisfiability problem in a straightforward manner, our approach offers an umbrella under which many Petri net problems for conflict-free Petri nets can be shown to be solvable in polynomial time. As a side-product, our analysis provides evidence as to why detecting unboundedness for conflict-free Petri nets is easier (provided P ≠ NP) than for normal and sinkless Petri nets (which are two classes that properly contain that of conflict-free Petri nets).

This work was supported in part by the National Science Council of the Republic of China under Grants NSC-81-0408-E-002-01 and NSC-82-0408-E-002-025.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alimonti, P., Feuerstain, E. and Nanni, U. Linear time algorithms for liveness and boundedness in conflict-free Petri nets. Proceedings of 1st Latin American Theoretical Informatics (LATIN'92), LNCS 583, pp. 1–14, 1992.

    Google Scholar 

  2. Baker, H. Rabin's Proof of the Undecidability of the Reachability Set Inclusion Problem of Vector Addition Systems. Memo 79, MIT Project MAC, Computer Structure Group, 1973.

    Google Scholar 

  3. Crespi-Reghizzi, S. and Mandrioli, D. A decidability theorem for a class of vector addition systems. Information Processing Letters, 3(3):78–80, 1975.

    Google Scholar 

  4. Desel, J. and Esparza, J. Reachability in reversible free choice systems. Proceedings of the 8th Symposium on Theoretical Aspects of Computer Science (STACS'91), LNCS 480, pp. 384–397, 1991.

    Google Scholar 

  5. Esparza, J. A solution to the covering problem for 1-bounded conflict-free Petri nets. Information Processing Letters, 41(6):313–319, 1992.

    Google Scholar 

  6. Esparza, J. and Silva, M. A polynomial-time algorithm to decide liveness of bounded free choice nets. Theoret. Comp. Sci., 102:185–205, 1992.

    Google Scholar 

  7. Garey, M. and Johnson, D. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman & Company Publishers, San Francisco, California, 1979.

    Google Scholar 

  8. Grabowski, J. The decidability of persistence for vector addition systems. Information Processing Letters, 11(1):20–23, 1980.

    Google Scholar 

  9. Hack, M. The equality problem for vector addition systems is undecidable. Theoret. Comp. Sci., 2:77–95, 1976.

    Google Scholar 

  10. Heiner, M. Petri net based software validation prospects and limitations. International Computer Science Institute, Berkeley, California. TR-92-022, March, 1992.

    Google Scholar 

  11. Hopcroft, J. and Pansiot, J. On the reachability problem for 5-dimensional vector addition systems. Theoret. Comp. Sci., 8:135–159, 1979.

    Google Scholar 

  12. Howell, R. and Rosier, L. Completeness results for conflict-free vector replacement systems. J. of Computer and System Sciences, 37:349–366, 1988.

    Google Scholar 

  13. Howell, R. and Rosier, L. On questions of fairness and temporal logic for conflictfree Petri nets. In G. Rozenberg, editor, Advances in Petri Nets 1988, pages 200–226, Springer-Verlag, Berlin, 1988. LNCS 340.

    Google Scholar 

  14. Howell, R., Rosier, L., Huynh, D. and Yen, H. Some complexity bounds for problems concerning finite and 2-dimensional vector addition systems with states. Theoret. Comp. Sci., 46:107–140, 1986.

    Google Scholar 

  15. Howell, R., Rosier, L. and Yen, H. An O(n1.5) algorithm to decide boundedness for conflict-free vector replacement systems. Information Processing Letters, 25:27–33, 1987.

    Google Scholar 

  16. Howell, R., Rosier, L. and Yen, H. A taxonomy of fairness and temporal logic problems for Petri nets. Theoret. Comp. Sci., 82:341–372, 1991.

    Google Scholar 

  17. Howell, R., Rosier, L. and Yen, H. Normal and sinkless Petri nets, in ‘Proceedings of the 7th International Conference on the Fundamentals of Computation Theory,’ pp. 234–243, 1989. To appear in J. of Computer and System Sciences, 46, 1993.

    Google Scholar 

  18. Jones, N., Landweber, L. and Lien, Y. Complexity of some problems in Petri nets. Theoret. Comp. Sci., 4:277–299, 1977.

    Google Scholar 

  19. Khachian, L. A polynomial algorithm for linear programming. Doklady Akad. Nauk USSR, 244, no. 5(1979), 1093–96. Translated in Soviet Math. Doklady, 20, 191–94.

    Google Scholar 

  20. Kosaraju, R. Decidability of reachability in vector addition systems. In Proceedings of the 14th Annual ACM Symposium on Theory of Computing, pp. 267–280, 1982.

    Google Scholar 

  21. Lipton, R. The reachability problem requires exponential space. Technical Report 62, Yale University, Dept. of CS., Jan. 1976.

    Google Scholar 

  22. Landweber, L. and Robertson, E. Properties of conflict-free and persistent Petri nets. JACM, 25(3):352–364, 1978.

    Google Scholar 

  23. Mayr, E. An algorithm for the general Petri net reachability problem. SIAM J. Comput., 13(3):441–460, 1984. A preliminary version of this paper was presented at the 13th Annual Symposium on Theory of Computing, 1981.

    Google Scholar 

  24. Murata, T. Petri nets: properties, analysis and applications. Proc. of the IEEE, 77(4): 541–580, 1989.

    Google Scholar 

  25. Peterson, J. Petri Net Theory and the Modeling of Systems. Prentice Hall, Englewood Cliffs, NJ, 1981.

    Google Scholar 

  26. Rackoff, C. The covering and boundedness problems for vector addition systems. Theoret. Comp. Sci., 6:223–231, 1978.

    Google Scholar 

  27. Reisig, W. Petri Nets: An Introduction. Springer-Verlag, Heidelberg, 1985.

    Google Scholar 

  28. Suzuki, I. and Kasami, T. Three measures for synchronic dependence in Petri nets, Acta Informatica, 19:325–338, 1983.

    Google Scholar 

  29. Silva, M. and Murata, T. B-Fairness and structural B-Fairness in Petri net models of concurrent systems J. of Computer and System Sciences, 44:447–477, 1992.

    Google Scholar 

  30. Stockmeyer, L. The polynomial-time hierarchy. Theoret. Comp. Sci., 3:1–22, 1977.

    Google Scholar 

  31. Valk, R. and Jantzen, M. The residue of vector sets with applications to decidability problems in Petri nets, Acta Informatica, 21:643–674, 1985.

    Google Scholar 

  32. Yamasaki, H. Normal Petri nets. Theoret. Comp. Sci., 31:307–315, 1984.

    Google Scholar 

  33. Yen, H. A polynomial time algorithm to decide pairwise concurrency of transitions for 1-bounded conflict-free Petri nets. Information Processing Letters, 38:71–76, 1991.

    Google Scholar 

  34. Yen, H. A unified approach for deciding the existence of certain Petri net paths. Information and Computation, 96(1): 119–137, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Electrical Engineering, National Taiwan University, Taipei, Taiwan, ROC

    Hsu-Chun Yen, Bow-Yaw Wang & Ming-Sheng Yang

Authors
  1. Hsu-Chun Yen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bow-Yaw Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ming-Sheng Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Marco Ajmone Marsan

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yen, HC., Wang, BY., Yang, MS. (1993). A unified approach for reasoning about conflict-free Petri nets. In: Ajmone Marsan, M. (eds) Application and Theory of Petri Nets 1993. ICATPN 1993. Lecture Notes in Computer Science, vol 691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56863-8_64

Download citation

  • DOI: https://doi.org/10.1007/3-540-56863-8_64

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56863-6

  • Online ISBN: 978-3-540-47759-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation