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Nondeterministic Probabilistic Petri Net — A New Method to Study Qualitative and Quantitative Behaviors of System

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Abstract

There are many variants of Petri net at present, and some of them can be used to model system with both function and performance specification, such as stochastic Petri net, generalized stochastic Petri net and probabilistic Petri net. In this paper, we utilize extended Petri net to address the issue of modeling and verifying system with probability and nondeterminism besides function aspects. Using probabilistic Petri net as reference, we propose a new mixed model NPPN (Nondeterministic Probabilistic Petri Net) system, which can model and verify systems with qualitative and quantitative behaviours. Then we develop a kind of process algebra for NPPN system to interpret its algebraic semantics, and an action-based PCTL (Probabilistic Computation Tree Logic) to interpret its logical semantics. Afterwards we present the rules for compositional operation of NPPN system based on NPPN system process algebra, and the model checking algorithm based on the action-based PCTL. In order to put the NPPN system into practice, we develop a friendly and visual tool for modeling, analyzing, simulating, and verifying NPPN system using action-based PCTL. The usefulness and effectiveness of the NPPN system are illustrated by modeling and model checking an elaborate model of travel arrangements workflow.

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References

  1. Girault C, Valk R. Petri Nets for System Engineering: A Guide to Modeling, Verification, and Application. Springer-Verlag, 2003.

  2. Lin C. Stochastic Petri Net and System Performance Evaluation (2nd Edition). Tsinghua University Press, 2005, pp.1–2. (in Chinese)

  3. Noe J D, Nutt G J. Macro e-nets representation of parallel systems. IEEE Transactions on Computers, 1973, C-22(8): 718–727.

    Article  Google Scholar 

  4. Merlin P M, Farber D J. Recoverability of communication protocols: Implications of a theoretical study. IEEE Transactions on Communications, 1976, 24(9): 1036–1043.

    Article  MathSciNet  MATH  Google Scholar 

  5. Molloy M K. On the integration of delay and throughput measures in distributed processing models [Ph.D. Thesis]. University of California, Los Angeles, USA, 1981.

  6. Natkin S. Les reseaux de PETRI stochastiques et leur application à l’évaluation des systèmes informatiques [Ph.D. Thesis]. CNAM, Paris, France, 1980. (In French)

  7. Symons F JW. Introduction to numerical Petri nets, a general graphical model of concurrent processing systems. Australian Telecommunications Research, 1980, 14(1): 28–33.

    Google Scholar 

  8. Marsan M A, Conte G, Balbo G. A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Transactions on Computer Systems, 1984, 2(2): 93–122.

    Article  Google Scholar 

  9. Petri C A. Introduction to general net theory. In Lecture Notes in Computer Science 84, Brauer W (ed.), Springer-Verlag, 1980, pp.1–19.

  10. Balbo G. Introduction to generalized stochastic Petri net. In Proc. the 7th Int. Conf. Formal Methods for Performance Evaluation, May 2007, pp.83–131.

  11. Baier C, Katoen J P. Principles of Model Checking. MIT Press, 2008.

  12. Albanese M, Chellappa R, Moscato V, Picariello A, Subrahmanian V S, Turaga P, Udrea O. A constrained probabilistic Petri net framework for human activity detection in video. IEEE Transactions on Multimedia, 2008, 10(8): 1429–1443.

    Article  Google Scholar 

  13. Kudlek M. Probability in Petri nets. Fundamenta Informaticae — Concurrency Specification and Programming, 2005, 67(1/3): 121–130.

    MathSciNet  MATH  Google Scholar 

  14. Benveniste A, Fabre E, Haar S. Markov nets: Probabilistic models for distributed and concurrent systems. IEEE Transactions on Automatic Control, 2003, 48(11): 1936–1950.

    Article  MathSciNet  Google Scholar 

  15. Segala R. Modeling and verification of randomized distributed real-time systems [Ph.D. Thesis]. Massachusetts Institute of Technology, Cambridge, USA, 1995.

  16. Yuan C Y. Principle and Application of Petri Net. Beijing: Publishing House of Electronics Industry, 2005, pp.66–78. (in Chinese)

  17. Han T T. Diagnosis, synthesis and analysis of probabilistic models [Ph.D. Thesis]. RWTH Aachen University, Germany, 2009.

  18. Ash R B, Doléans-Dade C A. Probability and Measure Theory (2nd edition). Academic Press, 2000, pp.3–10.

  19. Milner R. Communication and Concurrency. Prentice-Hall, 1989, pp.10–36.

  20. Hoare C A R. Communicating Sequential Processes. Prentice-Hall, 1985, pp.81–100.

  21. Heljanko K, Junttila T, Latvala T. Incremental and complete bounded model checking for full PLTL. In Proc. the 17th International Conference on Computer Aided Verification, July 2005, pp.98–111.

  22. Hansson H, Jonsson B. A logic for reasoning about time and reliability. Formal Aspects of Computing, 1994, 6(5): 512–535.

    Article  MATH  Google Scholar 

  23. Bianco A, de Alfaro L. Model checking of probabilistic and nondeterministic systems. In Proc. the 15th Conference on Foundations of Software Technology and Theoretical Computer Science, December 1995, pp.499–513.

  24. Emerson E A, Mok A K, Sistla A P, Srinivasan J. Quantitative temporal reasoning. Real Time Systems, 1992, 4(4): 331–352.

    Article  Google Scholar 

  25. Baier C, Katoen J P, Hermanns H. Approximate symbolic model checking of continuous-time Markov chains. In Proc. the 10th International Conference on Concurrency Theory, August 1999, pp.146–162.

  26. Kindler E, Vesper T. ESTL: A temporal logic for events and states. In Proc. the 19th International Conference of Application and Theory of Petri Nets, June 1998, pp.365–384.

  27. Feng L, Kwiatkowska M, Parker D. Compositional verification of probabilistic systems using learning. In Proc. the 7th International Conference on Quantitative Evaluation of Systems, September 2010, pp.133–142.

  28. Bonet P, Llado C M, Puijaner R, Knottenbelt W J. PIPE v2.5: A Petri net tool for performance modelling. In Proc. the 23rd Latin American Conference on Informatics, October 2007.

  29. Yuan C Y, ZhaoW, Zhang S K, Huang Y. A three-layer model for business processes: Process logic, case semantics and workflow management. Journal of Computer Science and Technology, 2007, 22(3): 410–425.

    Article  MathSciNet  Google Scholar 

  30. Varacca D. Probability, nondeterminism and concurrency: Two denotational models for probabilistic computation [Ph.D. Thesis]. University of Aarhus, Aarhus, Denmark, 2003.

  31. Varacca D, Völzer H, Winskel G. Probabilistic event structures and domains. Theoretical Computer Science — Concurrency Theory, 2006, 358(2): 173–199,

    Article  MATH  Google Scholar 

  32. Hermanns H. Interactive markov chains: The quest for quantified quality. In Lecture Notes in Computer Science 2428, 2002, pp.57–87.

  33. Neuhäusser M R. Model checking nondeterministic and randomly timed systems [Ph.D. Thesis]. RWTH Aachen University, Germany, 2010.

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Authors and Affiliations

  1. School of Computer Engineering and Science, Shanghai University, Shanghai, 200072, China

    Yang Liu, Huai-Kou Miao (Senior Member, CCF), Hong-Wei Zeng & Pan Liu

  2. School of Information Science and Technology, Taishan University, Taian, 271021, China

    Yang Liu & Yan Ma

  3. State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, 210093, China

    Yang Liu

Authors
  1. Yang Liu
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  2. Huai-Kou Miao
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  3. Hong-Wei Zeng
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  4. Yan Ma
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  5. Pan Liu
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Correspondence to Yang Liu.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 60970007, 61073050 and 61170044, the National Basic Research 973 Program of China under Grant No. 2007CB310800, the Shanghai Leading Academic Discipline Project of China under Grant No. J50103, and the Natural Science Foundation of Shandong Province of China under Grant No. ZR2012FQ013.

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Liu, Y., Miao, HK., Zeng, HW. et al. Nondeterministic Probabilistic Petri Net — A New Method to Study Qualitative and Quantitative Behaviors of System. J. Comput. Sci. Technol. 28, 203–216 (2013). https://doi.org/10.1007/s11390-013-1323-7

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  • DOI: https://doi.org/10.1007/s11390-013-1323-7

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