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Behavior relativity of Petri nets

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Abstract

This paper presents a novel methodology for modelling and analyzing of behavior relations of concurrent systems. The set of all firing sequences of a Petri net is an important tool for describing the dynamic behavior of concurrent systems. In this paper, the behavior relativity of two concurrent subsystems in their synchronous composition is presented. Such behavior relativities, includingControlled Relativity, United Relativity, Interactive Relativity andExclusive Relativity, are defined respectively. The properties of the relativities are discussed in detail. The analysis method for these properties is based on minimum T-invariants, when two sybsystems are live bounded Petri nets. A well-known example has also been analyaed using the new methodology to demonstrate the advantages of the proposed methodology.

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References

  1. Battiston E, Cindio F D, Mauri G. Modular algebraic nets to specify concurrent systems.IEEE Trans. Software Eng., 1996, 22(10): 689–705.

    Article  Google Scholar 

  2. Shatz S M, Mai K, Black C, Tu S. Design and implementation of a Petri net-based toolkit for Ada tasking analysis.IEEE Trans. Parallel and Distributed Systems, 1990, 1(4): 424–441.

    Article  Google Scholar 

  3. Shatz S M, Tu S, Murata T. An application of Petri net reduction for Ada tasking deadlock analysis.IEEE Trans. Parallel and Distributed Systems, 1996, 7(12): 1307–1322.

    Article  Google Scholar 

  4. Shatz S M, Cheng W K. A Petri net framework for automated static analysis of Ada tasking behavior.J. Systems and Software, 1988, 8: 343–359.

    Article  Google Scholar 

  5. Avrunin G, Wileden J. Describing and analyzing distributed software system designs.ACM Trans. Programming Lanquages and Systems, 1985, 7(3): 380–403.

    Article  Google Scholar 

  6. Willson R G, Krogh B H. Petri net tools for the specification and analysis of discrete controllers.IEEE Trans. Software Eng., 1990, 16(1): 39–50.

    Article  Google Scholar 

  7. Avrunin G, Buy U, Corbett J, Dillon L, Wileden J. Automated analysis of concurrent systems with the constrained expression toolset.IEEE Trans. Software Eng., 1991, 17(11): 1204–1222.

    Article  Google Scholar 

  8. Chen Y, Tsai W T, Chao D. Dependency analysis — A Petri net based technique for synthesizing large concurrent systems. IEEE Trans. Parallel and Distributed Systems, 1993, 4(4): 414–426.

    Article  Google Scholar 

  9. Datta A, Ghosh S. Synthesis of a class of deadlock-free Petri net.J. of ACM, 1984, 31(3): 486–506.

    Article  MATH  MathSciNet  Google Scholar 

  10. Morgan E T, Razouk R R. Interactive state-space analysis of concurrent systems.IEEE Trans. Software Eng., 1987, 13(10): 1080–1091.

    Article  Google Scholar 

  11. Dwyer M B, Clarke L A. A compact Petri net representation and its implications for analysis.IEEE Trans. Software Eng., 1996, 22(11): 794–811.

    Article  Google Scholar 

  12. Notomi M, Murata T. Hierarchical reachability graph of bounded Petri nets for concurrent-software analysis.IEEE Trans. Software Eng., 1994, 20(5): 325–336.

    Article  MATH  Google Scholar 

  13. Bucci G, Vicario E. Compositional validation of time-critical systems using communicating time Petri nets.IEEE Trans. Software Eng., 1991, 21(12): 969–992.

    Article  Google Scholar 

  14. Murata T. Petri nets: Properties, analysis and applications. InProc. IEEE, 1989, 77: 541–580.

  15. Murata T, Shenker B, Shatz S M. Detection of Ada static deablocks using Petri net invariants.IEEE Trans. Software Eng., 1991, 15(3): 314–326.

    Article  Google Scholar 

  16. Jiang C J, Wu Z H. Nets operations.J. of Comp. Sci. & Tech., 1992, 7(4): 333–344.

    Article  MATH  MathSciNet  Google Scholar 

  17. Jiang C J. Nets operations (II).J. of Comp. Sci. & Tech., 1995, 10(6): 509–517.

    Article  Google Scholar 

  18. Suzuki I, Lu H. Temporal Petri nets and their application to modelling and analysis of a handshake daisy chain arbiter.IEEE Trans. Comput., 1989, 38(5): 696–704.

    Article  Google Scholar 

  19. Suzuki I. Formal analysis of the alternating bit protocol by temporal Petri nets.IEEE Trans. Software Eng., 1990, 16(11): 1273–1281.

    Article  Google Scholar 

  20. Valmari A. Compositional state space generation.Lect. Notes in Comp. Sci. 674, Springer-Verlag, 1993, pp.427–457.

  21. Jiang Jet al. Real-time synchronisation of multiaxis high-speed machines, from SFC specification to Petri net verification. InIEEE Proc. on Syst. Eng. for Auto., 1976, 143(2): 164–170.

  22. Souissi Y. On liveness preservation by compositional of nets via a set of places.Lect. Notes in Comp. Sci. 524, Springer-Verlag, 1991, pp.227–295.

  23. Sisto R, Valenzano A. Mapping Petri nets with inhibitor Arcs onto basic LOTOS behavior expressions.IEEE Trans. Comput., 1995, 44(12): 1361–1370.

    Article  MATH  Google Scholar 

  24. Jiang C J, Lu W M. On properties of concurrent system based on Petri net language to appear inJ. of Software.

  25. Reising W. Introduction of Petri Net. Springer-Verlag, 1982.

  26. Murata T, Wu Z. Fair relation and modified synchronic distances in a Petri net.J. of the Franklin Inst., 1985, 320(2): 63–82.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Tongji University, 20092, Shanghai, P.R. China

    Jiang Changjun

  2. The School of Information Science and Engineering, Ningbo University, 315211, Ningbo, P.R. China

    Jiang Changjun

  3. Department of Computer Science and Technology, University of Shandong Science and Technology, 201719, Shandong, P.R. China

    Jiang Changjun

  4. Department of Information System, City University of Hong Kong, Kowloon, Hong Kong, P.R. China

    Wang Huaiqing & Liao Shaoyi

Authors
  1. Jiang Changjun
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  2. Wang Huaiqing
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  3. Liao Shaoyi
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Corresponding author

Correspondence to Jiang Changjun.

Additional information

Supported by projects of National Natural Science Foundation of China (Grant Nos. 69973029, 69933020), the National NKBRSF of China (Grant No. G1998030604), the National ‘863’ High-Tech Program of China (Grant No. 2001AA413020), Excellent Ph.D. Paper Author Foundation of China (Grant No. 19934), Project of Shanghai Science and Technology. Project of Shanghai Dawn Plan Foundation and Project of Shandong Provincial Excellent Young Scientist Foundation.

JIANG Changjun received the Ph.D. degree in computer science from the Institute of Automation, Chinese Academy of Science. He is a professor at the Department of Computer Science and Engineering, Shanghai Tongji University, China. His research areas include Petri nets, concurrent systems, model checking, and fuzy reasoning.

WANG Huaiqing received the Ph.D. degree in computer science from the University of Manchester, Manchester, U.K., in 1987. He is an associate pprofessor at the Department of Information Systems, City University of Hong Kong. he specializes in research and development of intelligent systems, web-based intelligent agents and their ebusiness applications, such as multi-agent supported financial monitoring systems, intelligent agent-based knowledge management systems, modeling, and intelligent web-based educational systems.

LIAO Shaoyi received the Ph.D. degree in information systems from Aix Marseillelil University in 1993. He is an assistant professor in the Department of Information Systems, City University of Hong Kong. His research areas include object-oriented modeling, systems and technology, user profiling in e-business, and data mining techniques and applications.

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Jiang, C., Wang, H. & Liao, S. Behavior relativity of Petri nets. J. Compt. Sci. & Technol. 17, 770–780 (2002). https://doi.org/10.1007/BF02960767

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  • DOI: https://doi.org/10.1007/BF02960767

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