Model Checking a Path

  • N. Markey
  • P. Schnoebelen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2761)


We consider the problem of checking whether a finite (or ultimately periodic) run satisfies a temporal logic formula. This problem is at the heart of “runtime verification” but it also appears in many other situations. By considering several extended temporal logics, we show that the problem of model checking a path can usually be solved efficiently, and profit from specialized algorithms. We further show it is possible to efficiently check paths given in compressed form.


Model Check Temporal Logic Kripke Structure Model Check Problem Temporal Formula 
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. [BBF+01]
    Bérard, B., Bidoit, M., Finkel, A., Laroussinie, F., Petit, A., Petrucci, L., Schnoebelen, P.: Systems and Software Verification. Model-Checking Techniques and Tools. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  2. [BCC+03]
    Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. In: Highly Dependable Software. Advances in Computers, vol. 58. Academic Press, London (2003)Google Scholar
  3. [CGP99]
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  4. [CM77]
    Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational databases. In: Proc. 9th ACM Symp. Theory of Computing (STOC 1977), Boulder, CO, USA, 1977, May 1977, pp. 77–90 (1977)Google Scholar
  5. [Dru00]
    Drusinsky, D.: The Temporal Rover and the ATG Rover. In: Havelund, K., Penix, J., Visser, W. (eds.) SPIN 2000. LNCS, vol. 1885, pp. 323–330. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. [DS02]
    Demri, S., Schnoebelen, P.: The complexity of propositional linear temporal logics in simple cases. Information and Computation 174(1), 84–103 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. [Eme90]
    Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. ch. 16, vol. B, pp. 995–1072. Elsevier Science, Amsterdam (1990)Google Scholar
  8. [FS01]
    Finkbeiner, B., Sipma, H.: Checking finite traces using alternating automata. In: Proc. 1st Int. Workshop on Runtime Verification (RV 2001), Paris, France, DK, July 2001. Electronic Notes in Theor. Comp. Sci., vol. 55(2), Elsevier Science, Amsterdam (2001)Google Scholar
  9. [GHR95]
    Greenlaw, R., Hoover, H.J., Ruzzo, W.L.: Limits to Parallel Computation: P-Completeness Theory. Oxford University Press, Oxford (1995)zbMATHGoogle Scholar
  10. [GPSS80]
    Gabbay, D.M., Pnueli, A., Shelah, S., Stavi, J.: On the temporal analysis of fairness. In: Proc. 7th ACM Symp. Principles of Programming Languages (POPL 1980), Las Vegas, NV, USA, 1980, January 1980, pp. 163–173 (1980)Google Scholar
  11. [Hav00]
    Havelund, K.: Using runtime analysis to guide model checking of Java programs. In: Havelund, K., Penix, J., Visser, W. (eds.) SPIN 2000. LNCS, vol. 1885, pp. 245–264. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. [HKP80]
    Harel, D., Kozen, D.C., Parikh, R.: Process logic: Expressiveness, decidability, completeness. In: Proc. 21st IEEE Symp. Foundations of Computer Science (FOCS 1980), Syracuse, NY, USA, 1980, October 1980, pp. 129–142 (1980)Google Scholar
  13. [HKV02]
    Harel, D., Kupferman, O., Vardi, M.Y.: On the complexity of verifying concurrent transition systems. Information and Computation 173(2), 143–161 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  14. [LMS02]
    Laroussinie, F., Markey, N., Schnoebelen, P.: Temporal logic with forgettable past. In: Proc. 17th IEEE Symp. Logic in Computer Science (LICS 2002), Copenhagen, Denmark, 2002, July 2002, pp. 383–392. IEEE Comp. Soc. Press, Los Alamitos (2002)CrossRefGoogle Scholar
  15. [LP02]
    Lassaigne, R., Peyronnet, S.: Approximate verification of probabilistic systems. In: Hermanns, H., Segala, R. (eds.) PROBMIV 2002, PAPM-PROBMIV 2002, and PAPM 2002. LNCS, vol. 2399, pp. 213–214. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. [Mar02]
    Markey, N.: Past is for free: on the complexity of verifying linear temporal properties with past. In: Proc. 9th Int. Workshop on Expressiveness in Concurrency (EXPRESS 2002), Brno, Czech Republic, August 2002. Electronic Notes in Theor. Comp. Sci., vol. 68.2. Elsevier Science, Amsterdam (2002)Google Scholar
  17. [MS03]
    Markey, N., Schnoebelen, P.: A PTIME-complete problem for SLPcompressed words (2003) (submitted for publication)Google Scholar
  18. [PR99]
    Plandowski, W., Rytter, W.: Complexity of language recognition problems for compressed words. In: Karhumaki, J., Maurer, H., Păun, G., Rozenberg, G. (eds.) Jewels are Forever, pp. 262–272. Springer, Heidelberg (1999)Google Scholar
  19. [Rab02]
    Rabinovich, A.: Expressive power of temporal logics. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 57–75. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. [RG01]
    Roger, M., Goubault-Larrecq, J.: Log auditing through model checking. In: Proc. 14th IEEE Computer Security Foundations Workshop (CSFW 2001), Cape Breton, Nova Scotia, Canada, 2001, June 2001, pp. 220–236. IEEE Comp. Soc. Press, Los Alamitos (2001)CrossRefGoogle Scholar
  21. [Ros82]
    Rosenstein, J.G.: Linear Orderings. Academic Press, London (1982)zbMATHGoogle Scholar
  22. [RP86]
    Rosner, R., Pnueli, A.: A choppy logic. In: Proc. 1st IEEE Symp. Logic in Computer Science (LICS 1986), Cambridge, MA, USA, 1986, June 1986, pp. 306–313. IEEE Comp. Soc. Press, Los Alamitos (1986)Google Scholar
  23. [SC85]
    Sistla, A.P., Clarke, E.M.: The complexity of propositional linear temporal logics. Journal of the ACM 32(3), 733–749 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  24. [Sch03]
    Schnoebelen, P.: The complexity of temporal logic model checking. In: Advances in Modal Logic, papers from 4th Int. Workshop on Advances in Modal Logic (AiML 2002), September-October 2002, Toulouse, France. World Scientific, Singapore (2003) (to appear)Google Scholar
  25. [Sto74]
    Stockmeyer, L.J.: The complexity of decision problems in automata and logic. PhD thesis, MIT (1974)Google Scholar
  26. [YS02]
    Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • N. Markey
    • 1
    • 2
  • P. Schnoebelen
    • 2
  1. 1.Lab. d’Informatique Fondamentale d’OrléansUniv. Orléans & CNRS
  2. 2.Lab. Spécification & VérificationENS de Cachan & CNRS

Personalised recommendations