Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3328))

Abstract

Monolithic finite-state probabilistic programs have been abstractly modeled by finite Markov chains, and the algorithmic verification problems for them have been investigated very extensively. In this paper we survey recent work conducted by the authors together with colleagues on he algorithmic verification of probabilistic procedural programs ([BKS,EKM04,EY04]). Probabilistic procedural programs can more naturally be modeled by recursive Markov chains ([EY04)], or equivalently, probabilistic pushdown automata ([EKM04)]. A very rich theory emerges for these models. While our recent work solves a number of verification problems for these models, many intriguing questions remain open.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alur, R., Etessami, K., Yannakakis, M.: Analysis of recursive state machines. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 304–313. Springer, Heidelberg (2001)

    Google Scholar 

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

    Google Scholar 

  3. Benedikt, M., Godefroid, P., Reps, T.: Model checking of unrestricted hierarchical state machines. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 652–666. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Besson, F., Jensen, T., Métayer, D.L., Thorn, T.: Model checking security properties of control flow graphs. Journal of Computer Security 9, 217–250 (2001)

    Google Scholar 

  5. Brázdil, T., Kučera, A., Stražovský, O.: Decidability of temporal properties of probabilistic pushdown automata. Technical report (in preparation)

    Google Scholar 

  6. Basu, S., Pollack, R., Roy, M.F.: On the combinatorial and algebraic complexity of quantifier elimination. Journal of the ACM 43(6), 1002–1045 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Booth, T.L., Thompson, R.A.: Applying probability measures to abstract languages. IEEE Transactions on Computers 22(5), 442–450 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  8. Canny, J.: Some algebraic and geometric computations in pspace. In: Proceedings of 20th ACM STOC, pp. 460–467 (1988)

    Google Scholar 

  9. Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Esparza, J., Hansel, D., Rossmanith, P., Schwoon, S.: Efficient algorithms for model checking pushdown systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 232–247. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  11. Esparza, J., Kučera, A., Mayr, R.: Model checking probabilistic pushdown automata. In: Proceedings of LICS 2004, pp. 12–21. IEEE Computer Society, Los Alamitos (2004), Full version: Tech. report FIMU-RS-2004-03, Masaryk University, Brno, available online at http://www.fmi.uni-stuttgart.de/szs/publications/info/esparza.EKM04rep.shtml.

  12. Etessami, K., Yannakakis, M.: Recursive markov chains, stochastic grammars, and monotone systems of non-linear equations. Technical report, School of Informatics, University of Edinburgh (2004)

    Google Scholar 

  13. Garey, M.R., Graham, R.L., Johnson, D.S.: Some NP-complete geometric problems. In: Proceedings of 8th ACM STOC, pp. 10–22 (1976)

    Google Scholar 

  14. Harris, T.E.: The Theory of Branching Processes. Springer, Heidelberg (1963)

    MATH  Google Scholar 

  15. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 512–535 (1994)

    Article  MATH  Google Scholar 

  16. Kučera, A.: Private communication (2004)

    Google Scholar 

  17. Kwiatkowska, M.: Model checking for probability and time: From theory to practice. In: Proceedings of LICS 2003, pp. 351–360. IEEE Computer Society Press, Los Alamitos (2003)

    Google Scholar 

  18. Mayr, R.: Private communication (2004)

    Google Scholar 

  19. Manning, C., Schütze, H.: Foundations of Statistical Natural Language Processing. MIT Press, Cambridge (1999)

    MATH  Google Scholar 

  20. Renegar, J.: On the computational complexity and geometry of the first-order theory of the reals. Parts I,II, III. Journal of Symbolic Computation, 255–352 (1992)

    Google Scholar 

  21. Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  22. Tiwari, P.: A problem that is easier to solve on the unit-cost algebraic RAM. Journal of Complexity, 393–397 (1992)

    Google Scholar 

  23. Vardi, M.: Automatic verification of probabilistic concurrent finite-state programs. In: Proceedings of FOCS 1985, pp. 327–338. IEEE Computer Society Press, Los Alamitos (1985)

    Google Scholar 

  24. 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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Esparza, J., Etessami, K. (2004). Verifying Probabilistic Procedural Programs. In: Lodaya, K., Mahajan, M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30538-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30538-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24058-7

  • Online ISBN: 978-3-540-30538-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics