Skip to main content

Model Checking Failure-Prone Open Systems Using Probabilistic Automata

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9364))

Abstract

We consider finite-state Hierarchical Probabilistic Automata (HPA) to model failure-prone open systems. In an HPA, its states are stratified into a fixed number of levels. A k-HPA is an HPA with \(k+1\) levels and it can be used to model open systems where up to k failures can occur. In this paper, we present a new forward algorithm that checks universality of a 1-HPA. This algorithm runs much faster than an earlier backward algorithm. We present the implementation and experimental results for verifying abstracted failure-prone web applications. We also prove a theoretical result showing that the problem of checking emptiness and universality for 2-HPA is undecidable answering an open question.

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

Buying options

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 EPUB and 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

Learn about institutional subscriptions

Notes

  1. 1.

    A rational number s has size r iff \(s=\frac{m}{n}\) where mn are integers, and the binary representation of m and n has at most r bits.

  2. 2.

    HPA tool website: https://github.com/benyue/HPA.

References

  1. Baier, C., Größer, M.: Recognizing \(\omega \)-regular languages with probabilistic automata. In: 20th IEEE Symposium on Logic in Computer Science, pp. 137–146 (2005)

    Google Scholar 

  2. Baier, C., Größer, M., Bertrand, N.: Probabilistic \(\omega \)-automata. J. ACM 59(1), 1–52 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Efficient computation of time-bounded reachability probabilities in uniform continuous-time markov decision processes. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 61–76. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Chadha, R., Sistla, A.P., Viswanathan, M.: Probabilistic Büchi automata with non-extremal acceptance thresholds. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 103–117. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Chadha, R., Sistla, A.P., Viswanathan, M.: Power of randomization in automata on infinite strings. Log. Methods Comput. Sci. 7(3), 1–22 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chadha, R., Sistla, A.P., Viswanathan, M., Ben, Y.: Decidable and expressive classes of probabilistic automata. In: Pitts, A. (ed.) FOSSACS 2015. LNCS, vol. 9034, pp. 200–214. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  7. Gimbert, H., Oualhadj, Y.: Probabilistic automata on finite words: decidable and undecidable problems. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 527–538. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Größer, M.: Reduction Methods for Probabilistic Model Checking. Ph.D. thesis, TU Dresden (2008)

    Google Scholar 

  9. Paz, A.: Introduction to Probabilistic Automata. Academic Press, Orlando (1971)

    MATH  Google Scholar 

  10. PRISM – Probabilistic Symbolic Model Checker. http://www.prismmodelchecker.org

  11. Rabin, M.O.: Probabilistic automata. Inf. Control 6(3), 230–245 (1963)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research is supported by the NSF grants CCF-1319754, CNS-1314485 and CNS-1035914.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yue Ben .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Ben, Y., Sistla, A.P. (2015). Model Checking Failure-Prone Open Systems Using Probabilistic Automata. In: Finkbeiner, B., Pu, G., Zhang, L. (eds) Automated Technology for Verification and Analysis. ATVA 2015. Lecture Notes in Computer Science(), vol 9364. Springer, Cham. https://doi.org/10.1007/978-3-319-24953-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24953-7_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24952-0

  • Online ISBN: 978-3-319-24953-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics