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A Characterization of Combined Traces Using Labeled Stratified Order Structures

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Applications and Theory of Petri Nets (PETRI NETS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6128))

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Abstract

This paper defines a class of labeled stratified order structures that characterizes exactly the notion of combined traces (i.e., comtraces) proposed by Janicki and Koutny in 1995. Our main technical contributions are the representation theorems showing that comtrace quotient monoid, combined dependency graph (Kleijn and Koutny 2008) and our labeled stratified order structure characterization are three different and yet equivalent ways to represent comtraces.

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References

  1. Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)

    Google Scholar 

  2. Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  3. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  4. Diekert, V.: On the Concatenation of Infinite Traces. In: Jantzen, M., Choffrut, C. (eds.) STACS 1991. LNCS, vol. 480, pp. 105–117. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  5. Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific, Singapore (1995)

    Google Scholar 

  6. Diekert, V., Métivier, Y.: Partial Commutation and Traces. In: Handbook of Formal Languages, Beyond Words, vol. 3, pp. 457–533. Springer, Heidelberg (1997)

    Google Scholar 

  7. Diekert, V., Horsch, M., Kufleitner, M.: On First-Order Fragments for Mazurkiewicz Traces. Fundam. Inform. 80(1-3), 1–29 (2007)

    MATH  MathSciNet  Google Scholar 

  8. Esparza, J., Heljanko, K.: Unfoldings – A Partial-Order Approach to Model Checking. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  9. Farzan, A., Madhusudan, P.: Causal Dataflow Analysis for Concurrent Programs. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 315–328. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Farzan, A., Madhusudan, P.: Causal Atomicity. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 102–116. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Fishburn, P.C.: Interval Orders and Interval Graphs. J. Wiley, New York (1985)

    MATH  Google Scholar 

  12. Gaifman, H., Pratt, V.: Partial Order Models of Concurrency and the Computation of Function. In: Proc. of LICS 1987, pp. 72–85 (1987)

    Google Scholar 

  13. Gastin, P.: Infinite Traces. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 277–308. Springer, Heidelberg (1990)

    Google Scholar 

  14. Gazagnaire, T., Genest, B., Hélouët, L., Thiagarajan, P.S., Yang, S.: Causal Message Sequence Charts. Theor. Comput. Sci. 410(41), 4094–4110 (2009)

    Article  MATH  Google Scholar 

  15. Janicki, R.: Relational Structures Model of Concurrency. Acta Informatica 45(4), 279–320 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  16. Janicki, R., Koutny, M.: Invariants and Paradigms of Concurrency Theory. In: Aarts, E.H.L., van Leeuwen, J., Rem, M. (eds.) PARLE 1991. LNCS, vol. 506, pp. 59–74. Springer, Heidelberg (1991)

    Google Scholar 

  17. Janicki, R., Koutny, M.: Structure of Concurrency. Theoretical Computer Science 112(1), 5–52 (1993)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  19. Janicki, R., Koutny, M.: Fundamentals of Modelling Concurrency Using Discrete Relational Structures. Acta Informatica 34, 367–388 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  20. Janicki, R., Koutny, M.: On Causality Semantics of Nets with Priorities. Fundamenta Informaticae 34, 222–255 (1999)

    MathSciNet  Google Scholar 

  21. Janicki, R., Lê, D.T.M.: Modelling Concurrency with Quotient Monoids. In: van Hee, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 251–269. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  22. Janicki, R., Lê, D.T.M.: Modelling Concurrency with Comtraces and Generalized Comtraces (submitted in 2009), http://arxiv.org/abs/0907.1722

  23. Juhás, G., Lorenz, R., Mauser, S.: Causal Semantics of Algebraic Petri Nets distinguishing Concurrency and Synchronicity. Fundamenta Informatica 86(3), 255–298 (2008)

    MATH  Google Scholar 

  24. Juhás, G., Lorenz, R., Mauser, S.: Synchronous + Concurrent + Sequential = Earlier Than + Not Later Than. In: Proc. of ACSD 2006, Turku, Finland, pp. 261–272. IEEE Press, Los Alamitos (2006)

    Google Scholar 

  25. Kleijn, H.C.M., Koutny, M.: Process Semantics of General Inhibitor Nets. Information and Computation 190, 18–69 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  26. Kleijn, J., Koutny, M.: Formal Languages and Concurrent Behaviour. Studies in Computational Intelligence 113, 125–182 (2008)

    Article  Google Scholar 

  27. Lê, D.T.M.: Studies in Comtrace Monoids, Master Thesis, Dept. of Computing and Software, McMaster University, Canada (August 2008)

    Google Scholar 

  28. Mazurkiewicz, A.: Concurrent Program Schemes and Their Interpretation, TR DAIMI PB-78, Comp. Science Depart., Aarhus University (1977)

    Google Scholar 

  29. Pratt, V.: Modeling concurrency with partial orders. International Journal of Parallel Programming 15(1), 33–71 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  30. Szpilrajn, E.: Sur l’extension de l’ordre partiel. Fund. Mathematicae 16, 386–389 (1930)

    MATH  Google Scholar 

  31. Thiagarajan, P.S., Walukiewicz, I.: An expressively complete linear time temporal logic for Mazurkiewicz traces. Inf. Comput. 179(2), 230–249 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Toronto, 10 King’s College Road, Toronto, ON, M5S 3G4, Canada

    Dai Tri Man Lê

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  1. Dai Tri Man Lê
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Editors and Affiliations

  1. Department of Information Technologies, Åbo Akademi University, Joukahainengatan 3-5, 20520, Turku, Finland

    Johan Lilius

  2. Institute of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237, Warsaw, Poland

    Wojciech Penczek

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Lê, D.T.M. (2010). A Characterization of Combined Traces Using Labeled Stratified Order Structures. In: Lilius, J., Penczek, W. (eds) Applications and Theory of Petri Nets. PETRI NETS 2010. Lecture Notes in Computer Science, vol 6128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13675-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-13675-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13674-0

  • Online ISBN: 978-3-642-13675-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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