Abstract

The classical model for concurrent systems is based on observing execution sequences of global states, separated from each other by atomic transitions. This model is intuitively simple and enjoys a variety of mathematical tools, e.g., finite automata and linear temporal logic, and algorithms that can be applied in order to test and verify concurrent systems. Although this model is sufficient for most frequently used validation tasks, some phenomena of concurrent systems are difficult to express using its related formalisms. In particular, not all the global states (snapshots) related to an execution appear on a particular execution sequence; some appear on equivalent sequences. Previous attempts to move into formalisms that are based on a more detailed model of execution, e.g,. the causality based model, resulted in specification formalisms with inherently high complexity verification algorithms. We study here verification problems that involve allowing the execution sequences model to observe past global states from equivalent executions. We show various algorithms and complexity results related to our extension of the interleaving model.

References

  1. 1.
    Alur, R., Chaudhuri, S., Etessami, K., Guha, S., Yannakakis, M.: Compression of Partially Ordered Strings. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 42–56. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Etessami, K., Yannakakis, M.: Realizability and Verification of MSC Graphs. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 797–808. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time Temporal Logic. JACM 49(5), 672–713 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Alur, R., McMillan, K., Peled, D.: Deciding Global Partial-Order Properties. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 41–52. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Alur, R., Peled, D., Penczek, W.: Model-Checking of Causality Properties. In: LICS 1995, pp. 90–100 (1995)Google Scholar
  6. 6.
    Chandy, K.M., Lamport, L.: Distributed Snapshots: Determining the Global State of Distributed Systems. ACM Transactions on Computer Systems 3, 63–75 (1985)CrossRefGoogle Scholar
  7. 7.
    Diekert, V., Gastin, P.: Local Temporal Logic is Expressively Complete for Cograph Dependence Alphabets. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, pp. 55–69. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Diekert, V., Gastin, P.: Pure Future Local Temporal Logics are Expressively Complete for Mazurkiewicz Traces. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 232–241. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Diekert, V., Rozenberg, G.: The Book of Traces. World Scientific, Singapore (1995)CrossRefGoogle Scholar
  10. 10.
    Emerson, E.A., Jutla, C.S.: The complexity of Tree Automata and Logics of Programs. In: FOCS 1988 (1988)Google Scholar
  11. 11.
    Garg, V.K., Waldecker, B.: Detecting Weak Unstable Predicates in Distributed Programs. IEEE Transactions on Parallel and Distributed Systems 5(3), 299–307 (1994)CrossRefGoogle Scholar
  12. 12.
    Gastin, P., Kuske, D.: Satisfiability and Model-Checking for MSO-definable Temporal Logics are in PSPACE. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 222–236. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Gastin, P., Mukund, M.: An Elementary Expressively Complete Temporal Logic for Mazurkiewicz Traces. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 938–949. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Gerth, R., Peled, D., Vardi, M., Wolper, P.: Simple on-the-fly Automatic Verification of Linear Temporal Logic. In: PSTV 1995, pp. 3–18 (1995)Google Scholar
  15. 15.
    Genest, B., Muscholl, A.: Pattern Matching and Membership for Hierarchical Message Sequence Charts. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 326–340. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Peled, D., Pnueli, A.: Proving Partial Order Liveness Properties. In: ICALP 1990, pp. 553–571 (1990)Google Scholar
  17. 17.
    Kuske, D.: Infinite Series-parallel Pomsets: Logic and Languages. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 648–662. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  18. 18.
    Mazurkiewicz, A.: Trace semantics. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 279–324. Springer, Heidelberg (1987)Google Scholar
  19. 19.
    Markey, N., Schnoebelen, P.: Model-checking a Path. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 251–265. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. 20.
    Peled, D.: Specification and Verification of Message Sequence Charts. In: FORTE/PSTV 2000, pp. 139–154 (2000)Google Scholar
  21. 21.
    Peled, D., Pnueli, A.: Proving Partial Order Properties. Theoretical Computer Science 126, 143–182 (1994)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Plandowski, W., Rytter, W.: Complexity of Language Recognition Problems for Compressed Words. In: Jewels are Forever, pp. 262–272. Springer, Heidelberg (1999)Google Scholar
  23. 23.
    Stoller, S., Liu, Y.A.: Efficient Symbolic Detection of Global Properties in Distributed Systems. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 357–368. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  24. 24.
    Thiagarajan, P.S., Walukiewicz, I.: An Expressively Complete Linear Time Temporal Logic for Mazurkiewicz Traces. Information and Computation 179(2), 230–249 (2002)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Vardi, M.Y., Wolper, P.: Reasoning About Infinite Computations. Information and Computation 115, 1–37 (1994)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Walukiewicz, I.: Difficult Configurations – On the Complexity of LTrL. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 140–151. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Blaise Genest
    • 1
  • Dietrich Kuske
    • 2
  • Anca Muscholl
    • 3
  • Doron Peled
    • 1
  1. 1.Department of Computer ScienceUniversity of WarwickCoventryUnited Kingdom
  2. 2.Institut für InformatikUniversität LeipzigLeipzigGermany
  3. 3.LIAFAUniversité Paris 7Paris Cedex 05France

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