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Computation of Minimal Siphons in Petri Nets by Using Binary Decision Diagrams

Published:01 January 2013Publication History
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Abstract

Siphons play an important role in the development of deadlock control methods by using Petri nets. The number of siphons increases exponentially with respect to the size of a Petri net. This article presents a symbolic approach to the computation of minimal siphons in Petri nets by using binary decision diagrams (BDD). The siphons of a Petri net can be found via a set of logic conditions. The logic conditions are symbolically modeled by using Boolean algebras. The operations of Boolean algebras are implemented by BDD that are capable of representing large sets of siphons with small shared data structures. The proposed method first uses BDD to compute all siphons of a Petri net and then a binary relation is designed to extract all minimal siphons. Finally, by using a number of examples, the efficiency of the proposed method is verified through different-sized problems.

References

  1. Andersen, H. R. 1997. An introduction to binary decision diagrams. Lecture notes for 49285 Advanced Algorithms E97, Department of Information Technology, Technical University of Denmark.Google ScholarGoogle Scholar
  2. Barkaoui, K. and Lemaire, B. 1989. An effective characterization of minimal deadlocks and traps in Petri nets based on graph theory. In Proceedings of the 10th International Conference on Application and Theory of Petri Nets. Springer, 1--21.Google ScholarGoogle Scholar
  3. Boer, E. R. and Murata, T. 1994. Generating basis siphons and traps of Petri nets using the sign incidence matrix. IEEE Trans. Circuits Syst. Regul. Pap. 41, 4, 266--271.Google ScholarGoogle ScholarCross RefCross Ref
  4. Brant, R. 1992. Symbolic Boolean manipulation with ordered binary decision diagrams. ACM Comput. Surv. 24, 3, 293--318. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Brown, F. M. 1990. Boolean Reasoning: The Logic of Boolean Equations. Kluwer Academic.Google ScholarGoogle ScholarCross RefCross Ref
  6. Cordone, R., Ferrarini, L., and Piroddi, L. 2005. Enumeration algorithms for minimal siphons in Petri nets based on place constraints. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 35, 6, 844--854. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Ezpeleta, J., Colom, J. M., and Martinez, J. 1995. A Petri net based deadlock prevention policy for flexible manufacturing systems. IEEE Trans. Rob. Autom. 11, 2, 173--184.Google ScholarGoogle ScholarCross RefCross Ref
  8. Ghaffari, A., Rezg, N., and Xie, X. L. 2003. Design of a live and maximally permissive petri net controller using the theory of regions. IEEE Trans. Rob. Autom. 19, 1, 137--142.Google ScholarGoogle ScholarCross RefCross Ref
  9. Hu, H. S. and Li, Z. W. 2008. An optimal-elementary-siphons based iterative deadlock prevention policy for flexible manufacturing systems. Int. J. Adv. Manuf. Technol. 38, 3--4, 309--320.Google ScholarGoogle ScholarCross RefCross Ref
  10. Hu, H. S. and Li, Z. W. 2009a. Efficient deadlock prevention policy in automated manufacturing systems using shared resources. Int. J. Adv. Manuf. Technol. 40, 5--6, 566--571.Google ScholarGoogle ScholarCross RefCross Ref
  11. Hu, H. S. and Li, Z. W. 2009b. Liveness enforcing supervision in video streaming systems using siphons. J. Inf. Sci. Eng. 25, 6, 1863--1884.Google ScholarGoogle Scholar
  12. Hu, H. S. and Li, Z. W. 2009c. Local and global deadlock prevention policies for resource allocation systems using partially generated reachability graphs. Comput. Ind. Eng. 57, 4, 1168--1181. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Hu, H. S. and Li, Z. W. 2009d. Modeling and scheduling for manufacturing grid workflows using timed petri nets. Int. J. Adv. Manuf. Technol. 42, 5--6, 553--568.Google ScholarGoogle ScholarCross RefCross Ref
  14. Hu, H. S., Zhou, M. C., and Li, Z. W. 2009. Liveness enforcing supervision of video streaming systems using non-sequential petri nets. IEEE Trans. Multimedia 11, 8, 1457--1465. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Huang, Y. S., Jeng, M. D., Xie, X. L., and Chung, S. L. 2001. Deadlock prevention based on petri nets and siphons. Int. J. Prod. Res. 39, 2, 283--305.Google ScholarGoogle ScholarCross RefCross Ref
  16. Huang, Y. S., Jeng, M. D., Xie, X. L., and Chung, D. H. 2006. Siphon-based deadlock prevention for flexible manufacturing systems. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 36, 6, 1248--1256. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Jeng, M. D. and Xie, X. L. 1984. Deadlock detection and prevention of automated manufacturing systems using Petri nets and siphons. In Deadlock Resolution in Computer-Integrated Systems, M. C. Zhou and M. P. Fanti Eds., Marcel-Dekker Inc., New York, 233--281.Google ScholarGoogle Scholar
  18. Kumaran, T. K., Chang, W., Cho, H., and Wysk, A. 1994. A structured approach to deadlock detection, avoidance and resolution in flexible manufacturing systems. Int. J. Prod. Res. 32, 10, 2361--2379.Google ScholarGoogle ScholarCross RefCross Ref
  19. Li, Z. W. and Shiptalni, M. 2009. Smart deadlock prevention policy for flexible manufacturing systems using petri nets. IET Control Theory Appl. 3, 3, 362--374.Google ScholarGoogle ScholarCross RefCross Ref
  20. Li, Z. W. and Zhou, M. C. 2004. Elementary siphons of petri nets and their application to deadlock prevention in flexible manufacturing systems. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 34, 1, 38--51. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Li, Z. W. and Zhou, M. C. 2006a. Clarifications on the definitions of elementary siphons of Petri nets. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 36, 6, 1227--1229. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Li, Z. W. and Zhou, M. C. 2006b. Two-stage method for synthesizing liveness-enforcing supervisors for flexible manufacturing systems using petri nets. IEEE Trans. Ind. Inf. 2, 4, 313--325.Google ScholarGoogle ScholarCross RefCross Ref
  23. Li, Z. W. and Zhou, M. C. 2008. Control of elementary and dependent siphons in petri nets and their application. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 38, 1, 133--148. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Li, Z. W. and Zhou, M. C. 2009. Deadlock Resolution in Automated Manufacturing Systems: A Novel Petri Net Approach. Springer. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Li, Z. W., Uzam, M., and Zhou, M. C. 2008. Deadlock control of concurrent manufacturing processes sharing finite resources. Int. J. Adv. Manuf. Technol. 38, 7--8, 787--800.Google ScholarGoogle ScholarCross RefCross Ref
  26. Li, Z. W., Zhou, M. C., and Jeng, M. D. 2008. A maximally permissive deadlock prevention policy for fms based on petri net siphon control and the theory of regions. IEEE Trans. Autom. Sci. and Eng. 5, 1, 182--188.Google ScholarGoogle ScholarCross RefCross Ref
  27. Lind-Nielsen, J. 2002. BuDDy: Binary decision diagram package release 2.2. IT-University of Copenhagen (ITU).Google ScholarGoogle Scholar
  28. Miner, A. S. and Ciardo, G. 1999. Efficient reachability set generation and storage using decision diagrams. In Proceedings of the 7th International Conference on Conceptual Structures. Lecture Notes in Computer Science, vol. 1639, 6--250. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Murata, T. 1989. Petri nets: Properties, analysis, and applications. Proc. IEEE 77, 4, 541--580.Google ScholarGoogle ScholarCross RefCross Ref
  30. Pastor, E., Roig, O., Cortadella, J., and Badia, R. M. 1994. Petri net analysis using boolean manipulation. In Proceedings of the 15th International Conference on Application and Theory of Petri Nets. Lecture Notes in Computer Science, vol. 815, 416--435. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Pastor, E., Cortadella, J., and Roig, O. 2001. Symbolic analysis of bounded petri nets. IEEE Trans. Comput. 50, 5, 432--448. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Piroddi, L., Cordone, R., and Fumagalli, I. 2008. Selective siphon control for deadlock prevention in Petri nets. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 38, 6, 1337--1348. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Piroddi, L., Cordone, R., and Fumagalli, I. 2009. Combined siphon and marking generation for deadlock prevention in Petri nets. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 39, 3, 650--661. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Starke, P. H. 2003. INA: Integrated Net Analyer. http://www2.informatik.huberlin.de/starke/ina.html.Google ScholarGoogle Scholar
  35. Uzam, M. and Zhou, M. C. 2006. An improved iterative syhthesis method for liveness enforcing supervisors of flexible manufacturing systems. Int. J. Prod. Res. 44, 10, 1987--2030.Google ScholarGoogle ScholarCross RefCross Ref
  36. Wang, A. R., Li, Z. W., Jia, J. Y., and Zhou, M. C. 2009. An effective algorithm to find elementary siphons in a class of petri nets. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 39, 4, 912--923. Google ScholarGoogle ScholarDigital LibraryDigital Library

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