Deciding global partial-order properties

  • Rajeev Alur
  • Ken McMillan
  • Doron Peled
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1443)


Model checking of asynchronous systems is traditionally based on the interleaving model, where an execution is modeled by a total order between events. Recently, the use of partial order semantics that allows independent events of concurrent processes to be unordered is becoming popular. Temporal logics that are interpreted over partial orders allow specifications relating global snapshots, and permit reduction algorithms to generate only one representative linearization of every possible partial-order execution during state-space search. This paper considers the satisfiability and the model checking problems for temporal logics interpreted over partially ordered sets of global configurations. For such logics, only undecidability results have been proved previously. In this paper, we present an Expspace decision procedure for a fragment that contains an eventuality operator and its dual. We also sharpen previous undecidability results, which used global predicates over configurations. We show that although our logic allows only local propositions (over events), it becomes undecidable when adding some natural until operator.


Partial Order Model Check Temporal Logic Causal Structure Atomic Proposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    R. Alur, W. Penczek, and D. Peled. Model-checking of causality properties. 10th Symposium on Logic in Computer Science, 90–100, 1995.Google Scholar
  2. 2.
    E.M. Clarke and E.A. Emerson. Design and synthesis of synchronization skeletons using branching time temporal logic. Workshop on Logic of Programs, LNCS 131, 52–71, 1981.MathSciNetGoogle Scholar
  3. 3.
    W. Ebinger. Logical definability of trace languages. In V. Diekert, G. Rozenberg (Eds.) The Book of Traces, World Scientific, 382–390, 1995.Google Scholar
  4. 4.
    J. Esparza. Model checking using net unfolding. Science of Computer Programming 23, 1994.Google Scholar
  5. 5.
    P. Godefroid and P. Wolper. A partial approach to model checking. Information and Computation 110 (2), 305–326, 1994.zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    S. Katz and D. Peled. Interleaving set temporal logic. Theoretical Computer Science 75, 21–43, 1992.Google Scholar
  7. 7.
    K. Lodaya, R. Parikh, R. Ramanujam, and P.S. Thiagarajan. A logical study of distributed transitions systems. Information and Computation 119, 91–118, 1985.MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Mazurkiewicz. Trace Theory. In W. Brauer, W. Reisig, G. Rozenberg (eds.), Advances in Petri Nets 1986, LNCS 255, 279–324, 1987.Google Scholar
  9. 9.
    K.L. McMillan. Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. Fourth CAV, LNCS 663, 164–177, 1992.Google Scholar
  10. 10.
    D. Peled. Combining partial order reductions with on-the-fly model checking. Sixth Conferenceon Computer Aided Verification, LNCS 818, 377–390, 1994.Google Scholar
  11. 11.
    W. Penczek. On undecidability of propositional temporal logics on trace systems. Information Processing Letters 43, 147–153, 1992.zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    V.R. Pratt. Modeling concurrency with partial orders. Intl. J. of Parallel Programming 15(1), 33–71, 1986.zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    P.S. Thiagarajan. A trace based extension of linear time temporal logic. Ninth Symposium on Logic in Computer Science, 1994.Google Scholar
  14. 14.
    P.S. Thiagarajan and I. Walukiewicz. An expressively complete linear time temporal logic for Mazurkiewicz traces. 12th Symposium on Logic in Computer Science, 1997.Google Scholar
  15. 15.
    A. Valmari. A Stubborn attack on state explosion. Proc. 2nd Conference on Computer-Aided Verification, LNCS 531, 156–165, 1990.Google Scholar
  16. 16.
    M.Y. Vardi and P. Wolper. An automata-theoretic approach to automatic program verification. First Symposium on Logic in Computer Science, 332–344, 1986.Google Scholar
  17. 17.
    I. Walukiewicz. Difficult configurations — on the complexity of LTrL. 25th International Colloquium on Automata, Languages, and Programming, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Rajeev Alur
    • 1
  • Ken McMillan
    • 2
  • Doron Peled
    • 3
  1. 1.University of Pennsylvania and Bell LaboratoriesUSA
  2. 2.Cadence Berkeley LabsUSA
  3. 3.Bell Laboratories and CMUUSA

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