Skip to main content

Inferring Network Invariants Automatically

  • Conference paper
Automated Reasoning (IJCAR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4130))

Included in the following conference series:

Abstract

Verification by network invariants is a heuristic to solve uniform verification of parameterized systems. Given a system P, a network invariant for P is a system that abstracts the composition of every number of copies of P running in parallel. If there is such a network invariant, by reasoning about it, uniform verification with respect to the family P[1] ∥ ⋯ ∥ P[n] can be carried out. In this paper, we propose a procedure that searches systematically for a network invariant satisfying a given safety property. The search is based on algorithms for learning finite automata due to Angluin and Biermann. We optimize the search by combining both algorithms for improving successive possible invariants. We also show how to reduce the learning problem to SAT, allowing efficient SAT solvers to be used, which turns out to yield a very competitive learning algorithm. The overall search procedure finds a minimal such invariant, if it exists.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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.

Similar content being viewed by others

References

  1. Krzysztof, R.: Apt and Dexter Kozen. Limits for automatic verification of finite-state concurrent systems. IPL 22(6), 307–309 (1986)

    Google Scholar 

  2. Alur, R., Madhusudan, P., Nam, W.: Symbolic compositional verification by learning assumptions. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 548–562. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Angluin, D.: Learning regaular sets from queries and counterexamples. IC 75, 87–106 (1987)

    MATH  MathSciNet  Google Scholar 

  4. Biermann, A.W., Feldman, J.A.: On the synthesis of finite-state machines from samples of their behaviour. IEEE TOC 21, 592–597 (1972)

    MATH  MathSciNet  Google Scholar 

  5. Berg, T., Jonsson, B., Leucker, M., Saksena, M.: Insights to Angluin’s learning. TR 2003-039, Uppsala University (2003)

    Google Scholar 

  6. Chaki, S., Clarke, E.M., Sinha, N., Thati, P.: Automated assume-guarrantee reasoning for simulation conformance. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 534–547. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Clarke, E.M., Talupur, M., Touili, T., Veith, H.: Verification by network decomposition. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 276–291. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Clarke, E.M., Talupur, M., Veith, H.: Environment abstraction for parameterized verification. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 126–141. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Emerson, E.A., Kahlon, V.: Reducing model checking of the many to the few. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 236–254. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. Emerson, E.A., Namjoshi, K.S.: Reasoning about rings. In: POPL (1995)

    Google Scholar 

  11. Gold, E.M.: Complexity of automaton identification from given data. IC 37(3), 302–320 (1978)

    MATH  MathSciNet  Google Scholar 

  12. Habermehl, P., Vojnar, T.: Regular model checking using inference of regular languages. ENTCS 138(3), 21–36 (2005)

    MathSciNet  Google Scholar 

  13. Jonsson, B., Nilsson, M.: Transitive closures of regular relations for verifying infinite-state systems. In: Schwartzbach, M.I., Graf, S. (eds.) ETAPS 2000 and TACAS 2000. LNCS, vol. 1785, Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Kurshan, R.P., McMillan, K.L.: A structural induction theorem for processes. IC 117(1), 1–11 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kesten, Y., Pnueli, A.: Control and data abstraction: The cornerstones of practical formal verification. STTT 2(4), 328–342 (2000)

    Article  MATH  Google Scholar 

  16. Kesten, Y., Piterman, N., Pnueli, A.: Bridging the gap between fair simulation and trace inclusion. IC 200(1), 35–61 (2005)

    MATH  MathSciNet  Google Scholar 

  17. Kesten, Y., Pnueli, A., Shahar, E., Zuck, L.: Network invariants in action. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, p. 2002. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Lang, K.J.: Random dfa’s can be approximately learned from sparse uniform examples. In: COLT, pp. 45–52 (1992)

    Google Scholar 

  19. Lesens, D., Halbwachs, N., Raymond, P.: Automatic verification of parameterized linear networks of processes. In: 24th POPL (1997)

    Google Scholar 

  20. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient sat solver. In: DAC, pp. 530–535. ACM Press, New York (2001)

    Google Scholar 

  21. Oncina, J., Garcia, P.: Inferring regular languages in polynomial update time. In: Pattern Recognition and Image Analysis. Series in Machine Perception and AI, vol. 1, pp. 49–61. World Scientific, Singapore (1992)

    Chapter  Google Scholar 

  22. Oliveira, A.L., Silva, J.P.M.: Efficient algorithms for the inference of minimum size dfas. Machine Learning 44(1/2), 93–119 (2001)

    Article  MATH  Google Scholar 

  23. Pena, J.M., Oliveira, A.L.: A new algorithm for the reduction of incompletely specified finite state machines. In: ICCAD, pp. 482–489 (1998)

    Google Scholar 

  24. Pnueli, A., Shahar, E.: A platform for combining deductive with algorithmic verification. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 184–195. Springer, Heidelberg (1996)

    Google Scholar 

  25. Pnueli, A., Shahar, E.: Liveness and acceleration in parameterized verification. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 328–343. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  26. Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Actively learning to verify safety for fifo automata. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 494–505. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  27. Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Learning to verify safety properties. In: Davies, J., Schulte, W., Barnett, M. (eds.) ICFEM 2004. LNCS, vol. 3308, pp. 274–289. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  28. Vardhan, A., Sen, K., Viswanathan, M., Agha, G.: Using language inference to verify omega-regular properties. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  29. Wolper, P., Lovinfosse, V.: Verifying properties of large sets of processes with network invariants. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, Springer, Heidelberg (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Grinchtein, O., Leucker, M., Piterman, N. (2006). Inferring Network Invariants Automatically. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_40

Download citation

  • DOI: https://doi.org/10.1007/11814771_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37187-8

  • Online ISBN: 978-3-540-37188-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics