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A Game-Theoretic Approach to Simulation of Data-Parameterized Systems

  • Orna Grumberg
  • Orna Kupferman
  • Sarai Sheinvald
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8837)

Abstract

This work focuses on data-parameterized abstract systems that extend standard modelling by allowing atomic propositions to be parameterized by variables that range over some infinite domain. These variables may range over process ids, message numbers, etc. Thus, abstract systems enable simple modelling of infinite-state systems whose source of infinity is the data. We define and study a simulation pre-order between abstract systems. The definition extends the definition of standard simulation by referring also to variable assignments. We define \(\textsc{vctl}^\star\) – an extension of \(\textsc{ctl}^\star\) by variables, which is capable of specifying properties of abstract systems. We show that \(\textsc{vctl}^\star\) logically characterizes the simulation pre-order between abstract systems. That is, that satisfaction of \(\textsc{vactl}^\star\), namely the universal fragment of \(\textsc{vctl}^\star\), is preserved in simulating abstract systems. For the second direction, we show that if an abstract system \({\cal{A}}_2\) does not simulate an abstract system \({\cal{A}}_1\), then there exists a \(\textsc{vactl}\) formula that distinguishes \({\cal{A}}_1\) from \({\cal{A}}_2\). Finally, we present a game-theoretic approach to simulation of abstract systems and show that the prover wins the game iff \({\cal{A}}_2\) simulates \({\cal{A}}_1\). Further, if \({\cal{A}}_2\) does not simulate \({\cal{A}}_1\), then the refuter wins the game and his winning strategy corresponds to a \(\textsc{vactl}\) formula that distinguishes \({\cal{A}}_1\) from \({\cal{A}}_2\). Thus, the many appealing practical advantages of simulation are lifted to the setting of data-parameterized abstract systems.

Keywords

Model Check Temporal Logic Winning Strategy Atomic Proposition Kripke Structure 
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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References

  1. 1.
    Paige, R., Bloom, B.: Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming 24, 189–220 (1996)MathSciNetGoogle Scholar
  2. 2.
    Bensalem, S., Bouajjani, A., Loiseaux, C., Sifakis, J.: Property preserving simulations. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 260–273. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  3. 3.
    Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data trees and XML reasoning. J. ACM 56(3), 1–48 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bojanczyk, M., Muscholl, A., Schwentick, T., Segoufin, L., David, C.: Two-variable logic on words with data. In: LICS 2006, pp. 7–16 (2006)Google Scholar
  5. 5.
    Browne, M.C., Clarke, E.M., Grumberg, O.: Characterizing finite Kripke structures in propositional temporal logic. Theoretical Computer Science 59, 115–131 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Cleaveland, R., Parrow, J., Steffen, B.: The concurrency workbench: A semantics-based tool for the verification of concurrent systems. ACM TOPLAS 15, 36–72 (1993)CrossRefGoogle Scholar
  8. 8.
    Damm, W., Pnueli, A.: Verifying out-of-order executions. In: Proc. 9th Conf. on Correct Hardware Design and Verification Methods, pp. 23–47. Chapman & Hall (1997)Google Scholar
  9. 9.
    Demri, S., D’Souza, D.: An automata-theoretic approach to constraint LTL. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 121–132. Springer, Heidelberg (2002)Google Scholar
  10. 10.
    German, S., Prasad Sistla, A.: Reasoning about systems with many processes. Journal of the ACM 39, 675–735 (1992)CrossRefzbMATHGoogle Scholar
  11. 11.
    Grumberg, O., Kupferman, O., Sheinvald, S.: Variable automata over infinite alphabets. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 561–572. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Grumberg, O., Kupferman, O., Sheinvald, S.: Model checking systems and specifications with parameterized atomic propositions. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 122–136. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Grumberg, O., Kupferman, O., Sheinvald, S.: An automata-theoretic approach to reasoning about parameterized systems and specifications. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 397–411. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  14. 14.
    Grumberg, O., Long, D.E.: Model checking and modular verification. In: Groote, J.F., Baeten, J.C.M. (eds.) CONCUR 1991. LNCS, vol. 527, pp. 250–265. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  15. 15.
    Grumberg, O., Long, D.E.: Model checking and modular verification. ACM Transactions on Programming Languagues and Systems 16(3), 843–871 (1994)CrossRefGoogle Scholar
  16. 16.
    Hallé, S., Villemaire, R., Cherkaoui, O.: Ctl model checking for labelled tree queries. In: TIME, pp. 27–35 (2006)Google Scholar
  17. 17.
    Henzinger, T.A., Kupferman, O., Rajamani, S.: Fair simulation. Information and Computation 173(1), 64–81 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kaminski, M., Zeitlin, D.: Extending finite-memory automata with non-deterministic reassignment. In: Csuhaj-Varjú, Ézik, Z.E. (eds.) AFL, pp. 195–207 (2008)Google Scholar
  19. 19.
    Kesten, Y., Piterman, N., Pnueli, A.: Bridging the gap between fair simulation and trace inclusion. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 381–393. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. 20.
    Lamport, L.: Specifying concurrent program modules. ACM Transactions on Programming Languagues and Systems 5, 190–222 (1983)CrossRefzbMATHGoogle Scholar
  21. 21.
    Lazić, R.S.: Safely freezing LTL. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 381–392. Springer, Heidelberg (2006)Google Scholar
  22. 22.
    Lynch, N.A., Tuttle, M.R.: Hierarchical correctness proofs for distributed algorithms. In: Proc. 6th ACM Symp. on Principles of Distributed Computing, pp. 137–151 (1987)Google Scholar
  23. 23.
    Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann (1996)Google Scholar
  24. 24.
    Milner, R.: An algebraic definition of simulation between programs. In: Proc. 2nd Int. Joint Conf. on Artificial Intelligence, pp. 481–489. British Computer Society (1971)Google Scholar
  25. 25.
    Neven, F., Schwentick, T., Vianu, V.: Towards regular languages over infinite alphabets. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 560–572. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  26. 26.
    Pnueli, A.: Applications of temporal logic to the specification and verification of reactive systems: A survey of current trends. In: Rozenberg, G., de Bakker, J.W., de Roever, W.-P. (eds.) Current Trends in Concurrency. LNCS, vol. 224, pp. 510–584. Springer, Heidelberg (1986)CrossRefGoogle Scholar
  27. 27.
    Graf, S., Saidi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  28. 28.
    Shemesh, Y., Francez, N.: Finite-state unification automata and relational languages. Information and Computation 114, 192–213 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: Proc. 5th ACM Symp. on Theory of Computing, pp. 1–9 (1973)Google Scholar
  30. 30.
    Tan, T.: Pebble Automata for Data Languages: Separation, Decidability, and Undecidability. PhD thesis, Technion - Computer Science Department (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Orna Grumberg
    • 1
  • Orna Kupferman
    • 2
  • Sarai Sheinvald
    • 2
  1. 1.Department of Computer ScienceThe TechnionHaifaIsrael
  2. 2.School of Computer Science and EngineeringHebrew UniversityJerusalemIsrael

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