Skip to main content
Springer Nature Link
Log in

Infinite State Model-Checking of Propositional Dynamic Logics

  • Conference paper
Computer Science Logic (CSL 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4207))

Included in the following conference series:

Abstract

Model-checking problems for PDL (propositional dynamic logic) and its extension PDL ∩  (which includes the intersection operator on programs) over various classes of infinite state systems (BPP, BPA, pushdown systems, prefix-recognizable systems) are studied. Precise upper and lower bounds are shown for the data/expression/combined complexity of these model-checking problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alur, R., Benedikt, M., Etessami, K., Godefroid, P., Reps, T.W., Yannakakis, M.: Analysis of recursive state machines. ACM Trans. Program. Lang. Syst. 27(4), 786–818 (2005)

    Article  Google Scholar 

  2. Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: Application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)

    Google Scholar 

  3. Blumensath, A.: Prefix-recognizable graphs and monadic second-order logic. Tech. Rep. 2001-06, RWTH Aachen, Germany (2001)

    Google Scholar 

  4. Cachat, T.: Uniform solution of parity games on prefix-recognizable graphs. ENTCS 68(6) (2002)

    Google Scholar 

  5. Caucal, D.: On infinite transition graphs having a decidable monadic theory. Theor. Comput. Sci. 290(1), 79–115 (2002)

    Article  MathSciNet  Google Scholar 

  6. Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. J. Assoc. Comput. Mach. 28(1), 114–133 (1981)

    MATH  MathSciNet  Google Scholar 

  7. Danecki, R.: Nondeterministic propositional dynamic logic with intersection is decidable. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 34–53. Springer, Heidelberg (1985)

    Google Scholar 

  8. Esparza, J.: On the decidabilty of model checking for several mu-calculi and petri nets. In: Tison, S. (ed.) CAAP 1994. LNCS, vol. 787, pp. 115–129. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  9. Esparza, J., Kucera, A., Schwoon, S.: Model checking LTL with regular valuations for pushdown systems. Inf. Comput. 186(2), 355–376 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18(2), 194–211 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  11. Göller, S., Lohrey, M.: Infinite State Model-Checking of Propositional Dynamic Logics Technical Report 2006/04, University of Stuttgart, Germany (2006), ftp://ftp.informatik.uni-stuttgart.de/pub/library/ncstrl.ustuttgart fi/TR2006-04/

    Google Scholar 

  12. Harel, D.: Recurring dominoes: making the highly undecidable highly understandable. Ann. Discrete Math. 24, 51–72 (1985)

    MATH  MathSciNet  Google Scholar 

  13. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. Foundations of computing. MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  14. Kupferman, O., Piterman, N., Vardi, M.: Model checking linear properties of prefix-recognizable systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 371–385. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Kupferman, O., Vardi, M.Y.: An automata-theoretic approach to reasoning about infinite-state systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 36–52. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  16. Lange, M.: Model checking propositional dynamic logic with all extras. J. Appl. Log. 4(1), 39–49 (2005)

    Article  Google Scholar 

  17. Lange, M., Lutz, C.: 2-Exptime lower bounds for propositional dynamic logics with intersection. J. Symb. Log. 70(4), 1072–1086 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Löding, C., Serre, O.: Propositional dynamic logic with recursive programs. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, pp. 292–306. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  19. Lugiez, D., Schnoebelen, P.: The regular viewpoint on PA-processes. Theor. Comput. Sci. 274(1–2), 89–115 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Mayr, R.: Strict lower bounds for model checking BPA. ENTCS 18 (1998)

    Google Scholar 

  21. Mayr, R.: Process rewrite systems. Inf. Comput. 156(1), 264–286 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. Mayr, R.: Decidability of model checking with the temporal logic EF. Theor. Comput. Sci. 256(1-2), 31–62 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  23. Muller, D., Schupp, P.: Alternating automata on infinite trees. Theor. Comput. Sci. 54(2-3), 267–276 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  24. Papadimitriou, C.H.: Computational Complexity. Addison Wesley, Reading (1994)

    MATH  Google Scholar 

  25. Thomas, W.: Some perspectives of infinite-state verification. In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 3–10. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Vardi, M.Y.: The complexity of relational query languages (extended abstract). In: Proc. STOC 1982, pp. 137–146. ACM Press, New York (1982)

    Google Scholar 

  27. Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  28. Walukiewicz, I.: Model checking CTL properties of pushdown systems. In: Kapoor, S., Prasad, S. (eds.) FST TCS 2000. LNCS, vol. 1974, pp. 127–138. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  29. Walukiewicz, I.: Pushdown processes: Games and model-checking. Inf. Comput. 164(2), 234–263 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  30. Wöhrle, S.: Decision problems over infinite graphs: Higher-order pushdown systems and synchronized products. Dissertation, RWTH Aachen, Germany (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FMI, Universität Stuttgart, Germany

    Stefan Göller & Markus Lohrey

Authors
  1. Stefan Göller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Markus Lohrey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain

    Zoltán Ésik

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Göller, S., Lohrey, M. (2006). Infinite State Model-Checking of Propositional Dynamic Logics. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_23

Download citation

  • DOI: https://doi.org/10.1007/11874683_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45458-8

  • Online ISBN: 978-3-540-45459-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics