Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Accelerating Interpolants

  • Conference paper
Automated Technology for Verification and Analysis (ATVA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7561))

  • 1078 Accesses

Abstract

We present Counterexample-Guided Accelerated Abstraction Refinement (CEGAAR), a new algorithm for verifying infinite-state transition systems. CEGAAR combines interpolation-based predicate discovery in counterexample-guided predicate abstraction with acceleration technique for computing the transitive closure of loops. CEGAAR applies acceleration to dynamically discovered looping patterns in the unfolding of the transition system, and combines overapproximation with underapproximation. It constructs inductive invariants that rule out an infinite family of spurious counterexamples, alleviating the problem of divergence in predicate abstraction without losing its adaptive nature. We present theoretical and experimental justification for the effectiveness of CEGAAR, showing that inductive interpolants can be computed from classical Craig interpolants and transitive closures of loops. We present an implementation of CEGAAR that verifies integer transition systems. We show that the resulting implementation robustly handles a number of difficult transition systems that cannot be handled using interpolation-based predicate abstraction or acceleration alone.

Supported by the Rich Model Toolkit initiative, http://richmodels.org , the Czech Science Foundation (projects P103/10/0306 and 102/09/H042), the Czech Ministry of Education (COST OC10009 and MSM 0021630528), the BUT project FIT-S-12-1 and the Microsoft Innovation Cluster for Embedded Software.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /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 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.

Similar content being viewed by others

References

  1. Albert, E., Arenas, P., Genaim, S., Puebla, G.: Closed-Form Upper Bounds in Static Cost Analysis. Journal of Automated Reasoning 46(2) (February 2011)

    Google Scholar 

  2. Ball, T., Podelski, A., Rajamani, S.K.: Relative Completeness of Abstraction Refinement for Software Model Checking. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 158–172. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  3. Bensalem, S., Lakhnech, Y.: Automatic generation of invariants. Form. Methods Syst. Des. 15(1), 75–92 (1999)

    Article  Google Scholar 

  4. Beyer, D., Cimatti, A., Griggio, A., Keremoglu, M.E., Sebastiani, R.: Software model checking via large-block encoding. In: FMCAD, pp. 25–32 (2009)

    Google Scholar 

  5. Beyer, D., Henzinger, T.A., Majumdar, R., Rybalchenko, A.: Path invariants. In: PLDI, pp. 300–309 (2007)

    Google Scholar 

  6. Blanc, R., Henzinger, T.A., Hottelier, T., Kovács, L.: ABC: Algebraic Bound Computation for Loops. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16. LNCS, vol. 6355, pp. 103–118. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Boigelot, B.: Symbolic Methods for Exploring Infinite State Spaces, PhD Thesis, vol. 189. Collection des Publications de l’Université de Liège (1999)

    Google Scholar 

  8. Bouajjani, A., Bozga, M., Habermehl, P., Iosif, R., Moro, P., Vojnar, T.: Programs with Lists Are Counter Automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 517–531. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Bozga, M., Habermehl, P., Iosif, R., Konečný, F., Vojnar, T.: Automatic Verification of Integer Array Programs. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 157–172. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Bozga, M., Iosif, R., Konečný, F.: Fast Acceleration of Ultimately Periodic Relations. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 227–242. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. Brillout, A., Kroening, D., Rümmer, P., Wahl, T.: An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 384–399. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Caniart, N., Fleury, E., Leroux, J., Zeitoun, M.: Accelerating Interpolation-Based Model-Checking. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 428–442. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Craig, W.: Linear reasoning. A new form of the Herbrand-Gentzen theorem. The Journal of Symbolic Logic 22(3), 250–268 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  14. Finkel, A., Leroux, J.: How to Compose Presburger-Accelerations: Applications to Broadcast Protocols. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 145–156. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Ganty, P., Majumdar, R.: Algorithmic verification of asynchronous programs. CoRR, abs/1011.0551 (2010)

    Google Scholar 

  16. Ginsburg, S., Spanier, E.: Bounded algol-like languages. Trans. of the AMS 113(2), 333–368 (1964)

    MathSciNet  MATH  Google Scholar 

  17. Graf, S., Saidi, H.: Construction of Abstract State Graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  18. Heizmann, M., Hoenicke, J., Podelski, A.: Refinement of Trace Abstraction. In: Palsberg, J., Su, Z. (eds.) SAS 2009. LNCS, vol. 5673, pp. 69–85. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from proofs. In: 31st POPL (2004)

    Google Scholar 

  20. Hojjat, H., Konečný, F., Garnier, F., Iosif, R., Kuncak, V., Rümmer, P.: A verification toolkit for numerical transition systems (tool paper). In: FM (2012)

    Google Scholar 

  21. Jhala, R., McMillan, K.L.: A Practical and Complete Approach to Predicate Refinement. In: Hermanns, H. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 459–473. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Kroening, D., Leroux, J., Rümmer, P.: Interpolating Quantifier-Free Presburger Arithmetic. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 489–503. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  23. McMillan, K.L.: An interpolating theorem prover. Theor. Comput. Sci. 345(1) (2005)

    Google Scholar 

  24. Monniaux, D.: Personal Communication

    Google Scholar 

  25. Rümmer, P.: A Constraint Sequent Calculus for First-Order Logic with Linear Integer Arithmetic. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 274–289. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  26. Rybalchenko, A., Sofronie-Stokkermans, V.: Constraint Solving for Interpolation. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 346–362. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  27. Smrčka, A., Vojnar, T.: Verifying Parametrised Hardware Designs Via Counter Automata. In: Yorav, K. (ed.) HVC 2007. LNCS, vol. 4899, pp. 51–68. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland

    Hossein Hojjat & Viktor Kuncak

  2. Verimag, Grenoble, France

    Radu Iosif & Filip Konečný

  3. Uppsala University, Sweden

    Philipp Rümmer

  4. Brno University of Technology, Czech Republic

    Filip Konečný

Authors
  1. Hossein Hojjat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Radu Iosif
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Filip Konečný
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Viktor Kuncak
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Philipp Rümmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Indian Institute of Technology, Computer Science and Engineering, Dept. of Computer Science and Engineering, IIT Bombay, Powai, 400076, Mumbai, Maharashtra, India

    Supratik Chakraborty

  2. Chennai Mathematical Institute, H1, SIPCOT IT Park, Kelambakkam, 603103, Siruseri, Tamil Nadu, India

    Madhavan Mukund

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hojjat, H., Iosif, R., Konečný, F., Kuncak, V., Rümmer, P. (2012). Accelerating Interpolants. In: Chakraborty, S., Mukund, M. (eds) Automated Technology for Verification and Analysis. ATVA 2012. Lecture Notes in Computer Science, vol 7561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33386-6_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33386-6_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33385-9

  • Online ISBN: 978-3-642-33386-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation