Skip to main content
Springer Nature Link
Log in

Abstraction and Refinement in Model Checking

  • Conference paper
Formal Methods for Components and Objects (FMCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4111))

Included in the following conference series:

  • 896 Accesses

Abstract

In this paper we survey abstraction and refinement in model checking. We restrict the discussion to existential abstraction which over-approximates the behaviors of the concrete model. The logics preserved under this abstraction are the universal fragments of branching-time temporal logics as well as linear-time temporal logics. For simplicity of presentation, we also restrict the discussion to abstraction functions, rather then abstraction relations. Thus, every concrete state is represented by exactly one abstract state. An abstract state then represents a set of concrete states, which is disjoint from the sets represented by other abstract states.

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

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. Ball, T., Rajamani, S.: Checking temporal properties of software with boolean programs. In: Proceedings of the Workshop on Advances in Verification (WAVE) (July 2000)

    Google Scholar 

  2. Beer, I., Ben-David, S., Eisner, C., Landver, A.: RuleBase: an industry-oriented formal verification tool. In: Proceedings of the 33rd Design Automation Conference (DAC 1996), pp. 655–660. IEEE Computer Society Press, Los Alamitos (1996)

    Chapter  Google Scholar 

  3. Beyer, D., Henzinger, T.A., Jhala, R., Majumdar, R.: Checking memory safety with blast. In: Cerioli, M. (ed.) FASE 2005. LNCS, vol. 3442, pp. 2–18. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Biere, A., Cimatti, A., Clarke, E.M., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: Proceedings of the 36rd Design Automation Conference (DAC 1999). IEEE Computer Society Press, Los Alamitos (1999)

    Google Scholar 

  5. Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without bdds. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, p. 193. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  6. Browne, M.C., Clarke, E.M., Grumberg, O.: Characterizing finite kripke structures in propositional temporal logic. Theor. Comp. Science 59(1–2) (July 1988)

    Google Scholar 

  7. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transaction on Computers 35(8), 677–691 (1986)

    Article  MATH  Google Scholar 

  8. Burch, J.R., Clarke, E.M., McMillan, K.L.: Symbolic model checking: 1020 states and beyond. Information and Computation 98, 142–170 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chaki, S., Clarke, E., Groce, A., Jha, S., Veith, H.: Modular verification of software components in C. In: International Conference on Software Engineering (ICSE), pp. 385–395 (2003)

    Google Scholar 

  10. Chauhan, P., Clarke, E.M., Kukula, J., Sapra, S., Veith, H., Wang, D.: Automated abstraction refinement for model checking large state spaces using SAT based conflict analysis. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Chauhan, P., Clarke, E.M., Kroening, D.: Using SAT based image computation for reachability analysis. Technical Report CMU-CS-03-151, Carnegie Mellon University, School of Computer Science (2003)

    Google Scholar 

  12. Cimatti, A., Clarke, E., Giunchiglia, F., Roveri, M.: NuSMV: a new symbolic model checker. Software Tools for Technology Transfer (1998)

    Google Scholar 

  13. Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Publishers, Cambridge (1999)

    Google Scholar 

  14. Clarke, E.M., Emerson, E.A.: Synthesis of synchronization skeletons for branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  15. Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstractio. In: Proceedings of the Nineteenth Annual ACM Symposium on Principles of Programming Languages. Association for Computing Machinery (January 1992)

    Google Scholar 

  16. Clarke, E., Kroening, D.: Hardware verification using ANSI-C programs as a reference. In: Proceedings of ASP-DAC 2003, pp. 308–311. IEEE Computer Society Press, Los Alamitos (2003)

    Google Scholar 

  17. Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. J. ACM 50(5), 752–794 (2003)

    MathSciNet  Google Scholar 

  18. Clarke, E.M., Gupta, A., Kukula, J., Strichman, O.: SAT based abstraction-refinement using ILP and machine leraning techniques. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 137–150. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  19. Clarke, E.M., Jha, S., Lu, Y., Veith, H.: Tree-like counterexamples in model checking. In: Seventeenth Annual IEEE Symposium on Logic In Computer Science (LICS), Copenhagen, Denmark (July 2002)

    Google Scholar 

  20. Copty, F., Fix, L., Fraer, R., Giunchiglia, E., Kamhi, G., Tacchella, A., Vardi, M.Y.: Benefits of bounded model checking at an industrial setting. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, p. 436. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  21. Corbett, J.C., Dwyer, M.B., Hatcliff, J., Laubach, S., Pasareanu, C.S.: Bandera: extracting finite-state models from java source code. In: International Conference on Software Engineering, pp. 439–448 (2000)

    Google Scholar 

  22. Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Transactions on Programming Languages and System (TOPLAS) 19(2) (1997)

    Google Scholar 

  23. Dams, D., Namjoshi, K.S.: The existence of finite abstractions for branching time model checking. In: Logic in Computer Science (LICS), pp. 335–344 (2004)

    Google Scholar 

  24. Eisner, C., Fisman, D., Havlicek, J., Lustig, Y., McIsaac, A., Van Campenhout, D.: Reasoning with temporal logic on truncated paths. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 27–39. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  25. Emerson, E.A., Halpern, J.Y.: “Sometimes” and “Not Never” revisited: On branching time versus linear time. J. ACM 33(1), 151–178 (1986)

    MATH  MathSciNet  Google Scholar 

  26. Fraer, R., Kamhi, G., Barukh, Z., Vardi, M.Y., Fix, L.: Prioritized traversal: Efficient reachability analysis for verification and falsification. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  27. Goldberg, E., Novikov, Y.: Berkmin: A fast and robust SAT-solver. In: DATE (2002)

    Google Scholar 

  28. 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)

    Google Scholar 

  29. Grumberg, O., Long, D.E.: Model checking and modular verification. ACM Trans. on Programming Languages and Systems 16(3), 843–871 (1994)

    Article  Google Scholar 

  30. Grumberg, O., Schuster, A., Yadgar, A.: Reachability using a memory-efficient all-solutions sat solver. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  31. Har’El, Z., Kurshan, R.P.: Software for analytical development of communications protocols. AT&T Technical Journal 69(1), 45–59 (1990)

    Google Scholar 

  32. Havelund, K., Pressburger, T.: Model checking JAVA programs using JAVA PathFinder. International Journal on Software Tools for Technology Transfer 2(4), 366–381 (2000)

    Article  MATH  Google Scholar 

  33. Holzmann, G.: Design and Validation of Computer Protocols. Prentice-Hall, Englewood Cliffs (1991)

    Google Scholar 

  34. Holzmann, G.: Logic verification of ansi-c code with SPIN. In: Havelund, K., Penix, J., Visser, W. (eds.) SPIN 2000. LNCS, vol. 1885, pp. 131–147. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  35. Kozen, D.: Results on the propositional μ-calculus. TCS 27 (1983)

    Google Scholar 

  36. Kurshan, R.P.: Computer-Aided Verification of coordinating processes - the automata theoretic approach. Princeton University Press, Princeton (1994)

    Google Scholar 

  37. Loiseaux, C., Graf, S., Sifakis, J., Bouajjani, A., Bensalem, S.: Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design 6, 11–45 (1995)

    Article  MATH  Google Scholar 

  38. Long, D.E.: Model Checking, Abstraction, and Compositional Reasoning. PhD thesis, Carnegie Mellon University (1993)

    Google Scholar 

  39. Marques-Silva, J.P., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48(5), 506–521 (1999)

    Article  MathSciNet  Google Scholar 

  40. McMillan, K.: Applications of craig interpolation to model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 1–12. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  41. McMillan, K.L.: Symbolic Model Checking: An Approach to the State Explosion Problem. PhD thesis, Carnegie Mellon University (1992)

    Google Scholar 

  42. McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Dordrecht (1993)

    MATH  Google Scholar 

  43. McMillan, K.L.: Interpolation and SAT-based model checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  44. McMillan, K.L.: Applying SAT methods in unbounded symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 250. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  45. Milner, R.: An algebraic definition of simulation between programs. In: Proc. 2nd Int. Joint Conf. on Artificial Intelligence, pp. 481–489. BCS (1971)

    Google Scholar 

  46. Milner, R.: An algebraic definition of simulation between programs. In: Proceedings of the Second Internation Joint Conference on Artificial Intelligence, pp. 481–489 (September 1971)

    Google Scholar 

  47. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: 39th Design Aotomation Conference (DAC 2001) (2001)

    Google Scholar 

  48. Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  49. Pnueli, A.: The Temporal Semantics of Concurrent Programs. Theoretical Computer Science 13, 45–60 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  50. Saidi, H., Shankar, N.: Abstract and model check while you prove. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 443–454. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  51. Sheeran, M., Singh, S., Staalmarck, G.: Checking safety properties using induction and a sat-solver. In: Johnson, S.D., Hunt Jr., W.A. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 108–125. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  52. Sheeran, M., Staalmarck, G.: A tutorial on stalmarck’s proof procedure for propositional logic. Formal Methods in System Design 16(1) (January 2000)

    Google Scholar 

  53. Shoham, S., Grumberg, O.: A game-based framework for CTL counterexamples and 3-valued abstraction-refinemnet. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 275–287. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, Technion, Haifa, 32000, Israel

    Orna Grumberg

Authors
  1. Orna Grumberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Centre for Mathematics and Computer Science, CWI, Kruislaan 413, 1098, Amsterdam, SJ, The Netherlands

    Frank S. de Boer

  2. Leiden Institute of Advanced Computer Science, Leiden University, P.O. Box 9512, 2300, Leiden, RA, The Netherlands

    Marcello M. Bonsangue

  3. Centre Equitation, VERIMAG, 2 Avenue de Vignate, 38610, Grenoble-Gières, France

    Susanne Graf

  4. Institute of Computer Science and Applied Mathematics, Christian-Albrechts University, Kiel,Hermann-Rodewald-Straße 3, 24118, Kiel, Germany

    Willem-Paul de Roever

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Grumberg, O. (2006). Abstraction and Refinement in Model Checking. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, WP. (eds) Formal Methods for Components and Objects. FMCO 2005. Lecture Notes in Computer Science, vol 4111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11804192_11

Download citation

  • DOI: https://doi.org/10.1007/11804192_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36749-9

  • Online ISBN: 978-3-540-36750-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics