Advertisement

Counting Models of Linear-Time Temporal Logic

  • Bernd Finkbeiner
  • Hazem Torfah
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)

Abstract

We investigate the model counting problem for safety specifications expressed in linear-time temporal logic (LTL). Model counting has previously been studied for propositional logic; in planning, for example, propositional model counting is used to compute the plan’s robustness in an incomplete domain. Counting the models of an LTL formula opens up new applications in verification and synthesis. We distinguish word and tree models of an LTL formula. Word models are labeled sequences that satisfy the formula. Counting the number of word models can be used in model checking to determine the number of errors in a system. Tree models are labeled trees where every branch satisfies the formula. Counting the number of tree models can be used in synthesis to determine the number of implementations that satisfy a given formula. We present algorithms for the word and tree model counting problems, and compare these direct constructions to an indirect approach based on encodings into propositional logic.

Keywords

Model counting temporal logic model checking synthesis tree automata 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bayardo, R.J., Schrag, R.: Using csp look-back techniques to solve real-world sat instances. In: AAAI/IAAI, pp. 203–208 (1997)Google Scholar
  2. 2.
    Biere, A.: Bounded model checking. In: Handbook of Satisfiability, pp. 457–481. IOS Press (2009)Google Scholar
  3. 3.
    Bloem, R.P., Gamauf, H.-J., Hofferek, G., Könighofer, B., Könighofer, R.: Synthesizing robust systems with RATSY. In: Association, O.P. (ed.) Proceedings First Workshop on Synthesis (SYNT 2012), vol. 84, pp. 47–53. Electronic Proceedings in Theoretical Computer Science (2012)Google Scholar
  4. 4.
    Bohy, A., Bruyère, V., Filiot, E., Jin, N., Raskin, J.-F.: Acacia+, a tool for LTL synthesis. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 652–657. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond (1992)Google Scholar
  6. 6.
    Darwiche, A.: New advances in compiling cnf into decomposable negation normal form. In: ECAI, pp. 328–332 (2004)Google Scholar
  7. 7.
    Ehlers, R.: Unbeast: Symbolic bounded synthesis. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 272–275. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Finkbeiner, B., Schewe, S.: Bounded synthesis. International Journal on Software Tools for Technology Transfer 15(5-6), 519–539 (2013)CrossRefGoogle Scholar
  9. 9.
    Gomes, C.P., Sabharwal, A., Selman, B.: Model counting. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 633–654. IOS Press, Amsterdam (2009), http://dblp.uni-trier.de/db/series/faia/faia185.html#GomesSS09
  10. 10.
    Kuhtz, L., Finkbeiner, B.: LTL path checking is efficiently parallelizable. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part II. LNCS, vol. 5556, pp. 235–246. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Kuhtz, L., Finkbeiner, B.: Weak kripke structures and LTL. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 419–433. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Kupferman, O., Lampert, R.: On the construction of fine automata for safety properties. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 110–124. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Littman, M.L., Majercik, S.M., Pitassi, T.: Stochastic boolean satisfiability. Journal of Automated Reasoning 27, 2001 (2000)MathSciNetGoogle Scholar
  14. 14.
    Morwood, D., Bryce, D.: Evaluating temporal plans in incomplete domains. In: AAAI (2012)Google Scholar
  15. 15.
    Pnueli, A.: The temporal logic of programs. In: Proceedings of the 18th Annual Symposium on Foundations of Computer Science, SFCS 1977, pp. 46–57. IEEE Computer Society, Washington, DC (1977), http://dx.doi.org/10.1109/SFCS.1977.32

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bernd Finkbeiner
    • 1
  • Hazem Torfah
    • 1
  1. 1.Reactive Systems GroupSaarland UniversitySaarbrückenGermany

Personalised recommendations