Model Checking LTLR Formulas under Localized Fairness

  • Kyungmin Bae
  • José Meseguer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7571)


Many temporal logic properties of interest involve both state and action predicates and only hold under suitable fairness assumptions. Temporal logics supporting both state and action predicates such as the Temporal Logic of Rewriting (TLR) can be used to express both the desired properties and the fairness assumptions. However, model checking such properties directly can easily become impossible for two reasons: (i) the exponential blowup in generating the Büchi automaton for the implication formula including the fairness assumptions in its condition easily makes such generation unfeasible; and (ii) often the needed fairness assumptions cannot even be expressed as propositional temporal logic formulas because they are parametric, that is, they correspond to universally quantified temporal logic formulas. Such universal quantification is succinctly captured by the notion of localized fairness; for example, fairness localized to the parameter o in object fairness conditions. We summarize the foundations and present the language design and implementation of the new Maude LTLR Model Checker under localized fairness. This is the first tool we are aware of which can model check temporal logic properties under parametric fairness assumptions.


Model Check Temporal Logic Linear Temporal Logic State Proposition Ground Instance 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bae, K., Meseguer, J.: The Linear Temporal Logic of Rewriting Maude Model Checker. In: Ölveczky, P.C. (ed.) WRLA 2010. LNCS, vol. 6381, pp. 208–225. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Bae, K., Meseguer, J.: State/Event-Based LTL Model Checking under Parametric Generalized Fairness. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 132–148. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    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
  4. 4.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  5. 5.
    Couvreur, J.-M., Duret-Lutz, A., Poitrenaud, D.: On-the-Fly Emptiness Checks for Generalized Büchi Automata. In: Godefroid, P. (ed.) SPIN 2005. LNCS, vol. 3639, pp. 169–184. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Transactions on Programming Languages and Systems 19, 253–291 (1997)CrossRefGoogle Scholar
  7. 7.
    Duret-Lutz, A., Poitrenaud, D., Couvreur, J.-M.: On-the-fly Emptiness Check of Transition-Based Streett Automata. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 213–227. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Henzinger, M.R., Telle, J.A.: Faster Algorithms for the Nonemptiness of Streett Automata and for Communication Protocol Pruning. In: Karlsson, R., Lingas, A. (eds.) SWAT 1996. LNCS, vol. 1097, pp. 16–27. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  10. 10.
    Holzmann, G., Peled, D., Yannakakis, M.: On nested depth first search (extended abstract). In: The Spin Verification System, pp. 23–32. American Mathematical Society (1996)Google Scholar
  11. 11.
    Holzmann, G.: The SPIN model checker: Primer and reference manual. Addison Wesley Publishing Company (2004)Google Scholar
  12. 12.
    Kesten, Y., Pnueli, A., Raviv, L., Shahar, E.: Model checking with strong fairness. Formal Methods in System Design 28(1), 57–84 (2006)zbMATHCrossRefGoogle Scholar
  13. 13.
    Kramer, J., Magee, J.: The evolving philosophers problem: Dynamic change management. IEEE Transactions on Software Engineering 16(11), 1293–1306 (2002)CrossRefGoogle Scholar
  14. 14.
    Latvala, T.: Model Checking LTL Properties of High-Level Petri Nets with Fairness Constraints. In: Colom, J.-M., Koutny, M. (eds.) ICATPN 2001. LNCS, vol. 2075, pp. 242–262. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Meseguer, J.: Localized Fairness: A Rewriting Semantics. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 250–263. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    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
  17. 17.
    Meseguer, J., Palomino, M., Martí-Oliet, N.: Equational abstractions. Theoretical Computer Science 403(2-3), 239–264 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Sun, J., Liu, Y., Dong, J.S., Pang, J.: PAT: Towards Flexible Verification under Fairness. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 709–714. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Vardi, M.Y.: Automata-Theoretic Model Checking Revisited. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 137–150. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

Personalised recommendations