Advertisement

The Linear Temporal Logic of Rewriting Maude Model Checker

  • Kyungmin Bae
  • José Meseguer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6381)

Abstract

This paper presents the foundation, design, and implementation of the Linear Temporal Logic of Rewriting model checker as an extension of the Maude system. The Linear Temporal Logic of Rewriting (LTLR) extends linear temporal logic with spatial action patterns which represent rewriting events. LTLR generalizes and extends various state-based and event-based logics and aims to avoid certain types of mismatches between a system and its temporal logic properties. We have implemented the LTLR model checker at the C++ level within the Maude system by extending the existing Maude LTL model checker. Our LTLR model checker provides very expressive methods to define event-related properties as well as state-related properties, or, more generally, properties involving both events and state predicates. This greater expressiveness is gained without compromising performance, because the LTLR implementation minimizes the extra costs involved in handling the events of systems.

Keywords

Model checking Rewriting Logic Maude Automata 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdulla, P., Annichini, A., Bouajjani, A.: Symbolic verification of lossy channel systems: Application to the bounded retransmission protocol. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 208–222. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Bae, K., Meseguer, J.: A rewriting-based model checker for the temporal logic of rewriting. In: Proc. 9th Inte. Workshop on Rule-Based Programming. ENTCS, Elsevier, Amsterdam (2008)Google Scholar
  3. 3.
    Baier, C., Katoen, J.P.: Principles of Model Checking. The MIT Press, Cambridge (2007)zbMATHGoogle Scholar
  4. 4.
    ter Beek, M.H., Fantechi, A., Gnesi, S., Mazzanti, F.: An action/state-based model-checking approach for the analysis of communication protocols for service-oriented applications. In: Leue, S., Merino, P. (eds.) FMICS 2007. LNCS, vol. 4916, pp. 133–148. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Chaki, S., Clarke, E., Grumberg, O., Ouaknine, J., Sharygina, N., Touili, T., Veith, H.: State/event software verification for branching-time specifications. In: Romijn, J.M.T., Smith, G.P., van de Pol, J. (eds.) IFM 2005. LNCS, vol. 3771, pp. 53–69. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Chaki, S., Clarke, E., Ouaknine, J., Sharygina, N., Sinha, N.: State/event-based software model checking. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 128–147. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Chaki, S., Clarke, E., Ouaknine, J., Sharygina, N., Sinha, N.: Concurrent software verification with states, events, and deadlocks. Formal Aspects of Computing 17, 461–483 (2005)CrossRefzbMATHGoogle Scholar
  8. 8.
    Chandy, K.M., Misra, J.: Parallel Program Design: a Foundation. Addison-Wesley, Reading (1988)zbMATHGoogle Scholar
  9. 9.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (2001)CrossRefGoogle Scholar
  10. 10.
    Clavel, M., Durán, F., Eker, S., Meseguer, J., Lincoln, P., Martí-Oliet, N., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  11. 11.
    Dershowitz, N., Jouannaud, J.P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 243–320. North-Holland, Amsterdam (1990)Google Scholar
  12. 12.
    Durán, F., Meseguer, J.: Maude’s module algebra. Science of Computer Programming 66, 125–153 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Eker, S., Meseguer, J., Sridharanarayanan, A.: The Maude LTL model checker. In: Gadducci, F., Montanari, U. (eds.) Proc. 4th. Intl. Workshop on Rewriting Logic and its Applications. ENTCS. Elsevier, Amsterdam (2002)Google Scholar
  14. 14.
    Eker, S., Meseguer, J., Sridharanarayanan, A.: The Maude LTL model checker and its implementation. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 230–234. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Fantechi, A., Gnesi, S., Lapadula, A., Mazzanti, F., Pugliese, R., Tiezzi, F.: A model checking approach for verifying cows specifications. In: Fiadeiro, J.L., Inverardi, P. (eds.) FASE 2008. LNCS, vol. 4961, pp. 230–245. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Fiadeiro, J., Martí-Oliet, N., Maibaum, T., Meseguer, J., Pita, I.: Towards a verification logic for rewriting logic. In: Bert, D., Choppy, C., Mosses, P.D. (eds.) WADT 1999. LNCS, vol. 1827, pp. 438–458. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  17. 17.
    Gastin, P., Oddoux, D.: Fast ltl to büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Gnesi, S., Mazzanti, F.: A model checking verification environment for uml statecharts. In: Proceedings XLIII AICA Annual Conference, University of Udine - AICA (2005), http://fmt.isti.cnr.it/WEBPAPER/gmaica2005.pdf
  19. 19.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. Journal of the Association for Computing Machinery 32(1), 137–172 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Holzmann, G., Peled, D., Yannakakis, M.: On nested depth first search (extended abstract). In: The Spin Verification System, pp. 23–32. American Mathematical Society, Providence (1996)Google Scholar
  21. 21.
    Huth, M., Jagadeesan, R., Schmidt, D.: Modal transition systems: A foundation for three-valued program analysis. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 155–169. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    Kindler, E., Vesper, T.: ESTL: A temporal logic for events and states. In: Desel, J., Silva, M. (eds.) ICATPN 1998. LNCS, vol. 1420, pp. 365–384. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  23. 23.
    Kozen, D.: Results on the propositional mu-calculus. Theoretical Computer Science 27, 333–354 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Lamport, L.: A temporal logic of actions. ACM Trans. on Prog. Lang. and Systems 16(3), 872–923 (1994)CrossRefGoogle Scholar
  25. 25.
    Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems – Specification. Springer, Heidelberg (1992)CrossRefzbMATHGoogle Scholar
  26. 26.
    Martí-Oliet, N., Pita, I., Fiadeiro, J.L., Meseguer, J., Maibaum, T.S.E.: A verification logic for rewriting logic. J. Log. Comput. 15(3), 317–352 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Meseguer, J.: The temporal logic of rewriting. Tech. Rep. UIUCDCS-R-2007-2815, CS Dept., University of Illinois at Urbana-Champaign (February 2007) (revised) (November 2007)Google Scholar
  28. 28.
    Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science 96(1), 73–155 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Meseguer, J.: The temporal logic of rewriting: A gentle introduction. In: Degano, P., De Nicola, R., Meseguer, J. (eds.) Concurrency, Graphs and Models. LNCS, vol. 5065, pp. 354–382. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  30. 30.
    Meseguer, J., Palomino, M., Martí-Oliet, N.: Equational abstractions. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 2–16. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  31. 31.
    Misra, J.: A Discipline of Multiprogramming. Springer, Heidelberg (2001)CrossRefzbMATHGoogle Scholar
  32. 32.
    Nicola, R.D., Vaandrager, F.W.: Action versus state based logics for transition systems. In: Guessarian, I. (ed.) LITP 1990. LNCS, vol. 469, pp. 407–419. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  33. 33.
    Pecheur, C., Raimondi, F.: Symbolic model checking of logics with actions. In: Edelkamp, S., Lomuscio, A. (eds.) MoChArt IV. LNCS (LNAI), vol. 4428, pp. 113–128. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  34. 34.
    Somenzi, F., Bloem, R.: Efficient büchi automata from ltl formulae. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 248–263. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  35. 35.
    Viry, P.: Equational rules for rewriting logic. Theoretical Computer Science 285, 487–517 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kyungmin Bae
    • 1
  • José Meseguer
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbana

Personalised recommendations