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A Generalisation of a Relational Structures Model of Concurrency

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Theoretical Aspects of Computing - ICTAC 2004 (ICTAC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3407))

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Abstract

We show how complex concurrent behaviours can be modelled by relational structures (\(X, \diamondsuit, \sqsubset\)), where X is a set (of event occurrences), \(\diamondsuit\) (interpreted as commutativity), \(\sqsubset\) (interpreted as weak causality) are binary relations on X. The paper is a continuation of the approach initiated in [6,18,1,9] substantially developed in [10,12], and recently partially generalized in [7]. For the first time an axiomatic model for the most general case is given. The results can be interpreted as a generalisation of Szpilrajn Theorem [25].

Partially supported by NSERC of Canada Grant.

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References

  1. Abraham, U., Ben-David, S., Magodor, M.: On global-time and inter-process communication. In: Semantics for Concurrency, Workshops in Computing, pp. 311–323. Springer, Heidelberg (1990)

    Google Scholar 

  2. Baldan, P., Busi, N., Corradini, A., Pinna, M.: Functorial Concurrent Semantics for Petri Nets with Read and Inhibitor Arcs, Theoretical Computer Science (to appear)

    Google Scholar 

  3. Best, E., de Boer, F., Palamedissi, C.: Partial Order and SOS Semantics for Linear Constraint Programs. In: Garlan, D., Le Métayer, D. (eds.) COORDINATION 1997. LNCS, vol. 1282, pp. 256–273. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  4. Best, E., Koutny, M.: Operational and Denotational Semantics for the Box Algebras. Theoretical Computer Science 211, 1–83 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Degano, P., Montanari, U.: Concurrent histories; a basis for observing distributed systems. J. Comput. System Sci. 34, 422–467 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gaifman, H., Pratt, V.: Partial order models of concurrency and the computation of functions. In: Proc. of LICS 1987, pp. 72–85

    Google Scholar 

  7. Guo, G., Janicki, R.: Modelling concurrent behaviours by commutativity and weak causality relations. In: Kirchner, H., Ringeissen, C. (eds.) AMAST 2002. LNCS, vol. 2422, pp. 178–191. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Fishburn, P.C.: Intransitive indifference with unequal indifference intervals. J. Math. Psych. 7, 144–149 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  9. Janicki, R., Koutny, M.: Invariants and Paradigms of Concurrency Theory. In: Aarts, E.H.L., Rem, M., van Leeuwen, J. (eds.) PARLE 1991. LNCS, vol. 505. Springer, Heidelberg (1991)

    Google Scholar 

  10. Janicki, R., Koutny, M.: Structure of Concurrency. Theoretical Computer Science 112, 5–52 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  11. Janicki, R., Koutny, M.: Semantics of Inhibitor Nets. Information and Computation 123(1), 1–16 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Janicki, R., Koutny, M.: Fundamentals of modelling concurrency using discrete relational structures. Acta Informatica 34, 367–388 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Janicki, R., Koutny, M.: On Causality Semantics of Nets with Priorities. Fundamenta Informaticae 38, 222–255 (1999)

    MathSciNet  Google Scholar 

  14. Juhás, G., Lorenz, R., Neumair, C.: Synthesis of controlled behavior with modules of signal nets. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 238–257. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  15. Katz, S., Peled, D.: Defining conditional independence using collapses. In: Semantics for Concurrency, Workshops in Computing, pp. 262–290. Springer, Heidelberg (1990)

    Google Scholar 

  16. Klaudel, H., Pommereau, F.: A Class of Composable and Preemptible High-Level Petri Nets witn and Application to a Multi-Tasking System. Fundamenta Informaticae 50, 33–55 (2002)

    MATH  MathSciNet  Google Scholar 

  17. Kleijn, J., Koutny, M.: Process semantics of P/T-nets with inhibitor arcs. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 261–281. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  18. Lamport, L.: The mutual exclusion problem: Part I - a theory of interprocess communication; Part II - statements and solutions. Journal of ACM 33(2), 313–326 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  19. Lamport, L.: What It Means for a Concurrent Programm to Satisfy a Specification: Why No One Has Specified Priority. In: Proc. 12th ACM Symp. on Programming Languages, pp. 78–83 (1985)

    Google Scholar 

  20. Mazurkiewicz, A.: Trace Theory. LNCS, vol. 225, pp. 297–324. Springer, Heidelberg (1986)

    Google Scholar 

  21. Milner, R.: Operational and Algebraic Semantics of Concurrent Processes. In: van Leuween, J. (ed.) Handbook of Theoretical Computer Science, vol. 2, pp. 1201–1242. Elsevier, Amsterdam (1993)

    Google Scholar 

  22. Pietkiewicz-Koutny, M.: The Synthesis Problem for Elementary Net Systems. Fundamenta Informaticae 40(2,3), 310–327 (1999)

    MathSciNet  Google Scholar 

  23. Plotkin, G., Pratt, V.: Teams can see pomsets. Stanford University, Stanford (1990) (Unpublished Memo)

    Google Scholar 

  24. Roux, O.H., Lime, D.: Time petri nets with inhibitor hyperarcs. Formal semantics and state space computation. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 371–390. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  25. Szpilrajn, E.: Sur l’extension de l’ordre partial. Fundamenta Mathematicae 16, 386–389 (1930)

    MATH  Google Scholar 

  26. Vogler, W.: Timed Testing of Concurrent Systems. Information and Computation 121, 149–171 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  27. Vogler, W.: Partial Order Semantics and Inhibitor Arcs. LNCS, vol. 1295, pp. 508–517. Springer, Heidelberg (1997)

    Google Scholar 

  28. Wollowski, R., Beister, J.: Precise Petri Net Modelling of Critical Races in Asynchronous Arbiters and Synchronizers. In: Proc. 1st Workshop on Hardware Design and Petri Nets, Lisbon, pp. 46–65 (1998)

    Google Scholar 

  29. Wollowski, R., Beister, J.: Comprehensive Causal Specification of Asynchronous Controller and Arbiter Behaviour. In: Yakovlev, A., Gomes, L., Lavagno, L. (eds.) Hardware Design and Petri Nets. Kluwer, Dordrecht (2000)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computing and Software, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    Ryszard Janicki

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  1. Ryszard Janicki
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Editors and Affiliations

  1. International Institute of Software Technology, United Nations University, Macau, China

    Zhiming Liu

  2. Department of Computer Science and Communication Engineering, Graduate School of Information Science and Electrical Engineering, Kyushu University, 6-10-1-Hakozaki, Higashi-ku, 812-8581, Fukuoka, Japan

    Keijiro Araki

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Janicki, R. (2005). A Generalisation of a Relational Structures Model of Concurrency. In: Liu, Z., Araki, K. (eds) Theoretical Aspects of Computing - ICTAC 2004. ICTAC 2004. Lecture Notes in Computer Science, vol 3407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31862-0_8

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  • DOI: https://doi.org/10.1007/978-3-540-31862-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25304-4

  • Online ISBN: 978-3-540-31862-0

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