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Maximal Confluent Processes

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Application and Theory of Petri Nets (PETRI NETS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7347))

Abstract

In process semantics of Petri Net, a non-sequential process is a concurrent run of the system represented in a partial order-like structure. For transition systems it is possible to define a similar notion of concurrent run by utilising the idea of confluence. Basically a confluent process is an acyclic confluent transition system that is a partial unfolding of the original system. Given a non-confluent transition system G, how to find maximal confluent processes of G is a theoretical problem having many practical applications.

In this paper we propose an unfolding procedure for extracting maximal confluent processes from transition systems. The key technique we utilise in the procedure is the construction of granular configuration structures (i.e. a form of event structures) based on diamond-structure information inside transition systems.

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References

  1. Badouel, E., Bernardinello, L., Darondeau, P.: The synthesis problem for elementary net systems is np-complete. Theor. Comput. Sci. 186(1-2), 107–134 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Best, E., Devillers, R.R.: Sequential and concurrent behaviour in petri net theory. Theor. Comput. Sci. 55(1), 87–136 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  3. Best, E., Fernández, C.: Nonsequential processes: a Petri net view. EATCS Monographs on TCS, vol. 13. Springer (1988)

    Google Scholar 

  4. Godefroid, P.: Partial-order Methods for the Verification of Concurrent Systems: an Approach to the State-explosion Problem. LNCS, vol. 1032. Springer, Heidelberg (1996)

    Book  Google Scholar 

  5. Goltz, U., Reisig, W.: The non-sequential behavior of petri nets. Information and Control 57(2/3), 125–147 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Groote, J.F., Sellink, M.P.A.: Confluence for process verification. Theoretical Computer Science 170(1-2), 47–81 (1996)

    MathSciNet  MATH  Google Scholar 

  7. Gunawardena, J.: Causal automata. TCS 101(2), 265–288 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hansen, H., Wang, X.: On the Origin of Events: Branching Cells as Stubborn Sets. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 248–267. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Liu, X., Walker, D.: Partial confluence of proceses and systems of objects. TCS 206(1-2), 127–162 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Milner, R.: Concurrency and Communication. Prentice-Hall (1988)

    Google Scholar 

  11. Peled, D.A.: All From One, One For All: On Model Checking Using Representatives. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 409–423. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  12. Sassone, V., Nielsen, M., Winskel, G.: Models for concurrency: Towards a classification. Theor. Comput. Sci. 170(1-2), 297–348 (1996)

    MathSciNet  MATH  Google Scholar 

  13. Valmari, A.: Stubborn Sets for Reduced State Space Generation. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 491–515. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  14. van Glabbeek, R.J., Plotkin, G.D.: Configuration structures, event structures and petri nets. Theoretical Computer Science 410(41), 4111–4159 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. van Glabbeek, R., Goltz, U.: Refinement of actions and equivalence notions for concurrent systems. Acta Informatica 37(4), 229–327 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. van Glabbeek, R.J., Plotkin, G.D.: Event Structures for Resolvable Conflict. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 550–561. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  17. Winskel, G.: Event Structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)

    Google Scholar 

  18. Winskel, G., Nielsen, M.: Models for concurrency. In: Handbook of Logic in Computer Science, vol. 4. Clarendon Press (1995)

    Google Scholar 

  19. Yakovlev, A., Kishinevsky, M., Kondratyev, A., Lavagno, L., Pietkiewicz-Koutny, M.: On the models for asynchronous circuit behaviour with or causality. FMSD 9(3), 189–233 (1996)

    Google Scholar 

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Wang, X. (2012). Maximal Confluent Processes. In: Haddad, S., Pomello, L. (eds) Application and Theory of Petri Nets. PETRI NETS 2012. Lecture Notes in Computer Science, vol 7347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31131-4_11

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  • DOI: https://doi.org/10.1007/978-3-642-31131-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31130-7

  • Online ISBN: 978-3-642-31131-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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