Skip to main content
Log in

Combining search space partition and abstraction for LTL model checking

  • Published:
Science in China Series F: Information Sciences Aims and scope Submit manuscript

Abstract

The state space explosion problem is still the key obstacle for applying model checking to systems of industrial size. Abstraction-based methods have been particularly successful in this regard. This paper presents an approach based on refinement of search space partition and abstraction which combines these two techniques for reducing the complexity of model checking. The refinement depends on the representation of each portion of search space. Especially, search space can be refined stepwise to get a better reduction. As reported in the case study, the integration of search space partition and abstraction improves the efficiency of verification with respect to the requirement of memory and obtains significant advantage over the use of each of them in isolation.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Clark E M, Grumberg O, Peled D et al. Model Checking. Cambridge, MA: The MIT Press, 1999

    Google Scholar 

  2. Clarke E M, Grumberg O, Jha S, et al. Counterexamples-guided abstraction refinement. In: Proceedings of 12th International Conference on Computer Aided Verification, LNCS 1855. Berlin: Springer, 2000. 154–169

    Chapter  Google Scholar 

  3. Gallardo M M, Merino P, Pimentel E. Refinement of LTL formulas for abstract model checking. In: Proceedings of 9th International Static Analysis Symposium, LNCS 2477. Berlin: Springer, 2002. 395–410

    Google Scholar 

  4. Gallardo M M, Merino P, Pimentel E. Comparing under-and over-approximations of LTL properties for model checking. In: Proceedings of 11th International Workshop on Functional and Logic Programming, ENTCS-76. Amsterdam: Elsevier, 2002

    Google Scholar 

  5. Gallardo M M, Merino P, Pimentel E. A tool for abstraction in model checking. In: Proceedings of 7th International Workshop on Formal Methods for Industral Critical Systems, ENTCS-76. Amsterdam: Elsevier, 2002

    Google Scholar 

  6. Clarke E M, Grumberg O, Long D. Model checking and abstraction. ACM Trans Program Lang Syst, 1994, 16(5): 1512–1542

    Article  Google Scholar 

  7. Gallardo M M, Merino P. A framework for automatic construction of abstract promela methods. In: Proceedings of 6th International SPIN Workshop on Model Checking of Software, LNCS 1680. Berlin: Springer, 1999. 184–199

    Google Scholar 

  8. Dams D, Gerth R, Grumberg O. Abstract interpretation of reactive systems. ACM Trans Program Lang Syst, 1997, 19(2): 253–291

    Article  Google Scholar 

  9. Ranzato, Scozzari F. Making abstract domains condensing. ACM Trans Comput Logic, 2005, 6(1): 33–60

    Article  MathSciNet  Google Scholar 

  10. Giacobazzi R, Ranzato F, Scozzari F. Making abstract interpretations complete. J ACM, 2000, 47(2): 361–416

    Article  MathSciNet  MATH  Google Scholar 

  11. Ranzato F, Tapparo F. An abstract interpretation-based refinement algorithm for strong preservation. In: Proceedings of the 11th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, LNCS 3440, Berlin: Springer, 2005. 140–156

    Google Scholar 

  12. Loiseaux C, Graf S, Sifakis J, et al. Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design, 1995, 23(5): 1–35

    Google Scholar 

  13. Gallardo M M, Martinez J, Merino P, et al. αSPIN: Extending SPIN with Abstraction. In: Proceedings of 9th International SPIN Workshop on Model Checking of Software, LNCS 2318. Berlin: Springer, 2002. 254–258

    Google Scholar 

  14. Holzmann G J. The SPIN Model Checker: Primer and Reference Manual. New York: Addison-Wesley, 2004

    Google Scholar 

  15. Berezin S, Campos S, Clarke E M. Compositional reasoning in model checking. In: Proceedings of International Symposium on Compositionality, LNCS 1536. Berlin: Springer, 1997. 81–102

    Google Scholar 

  16. McMillan K L. Verification of infinite state systems by compositional model checking. In: Proceedings of 10th International Conference on Correct Hardware Design and Verification Methods, LNCS 1703. Berlin: Springer, 1999. 219–234

    Google Scholar 

  17. Su B, Zhang W. Search space partition and case basis exploration for reducing model checking complexity. In: Proceedings of 2th International Symposium on Automated Technology on Verification and Analysis (ATVA’04), LNCS 3299. Berlin: Springer, 2004. 34–48

    Google Scholar 

  18. Zhang W. Combining static analysis and case-based search space partition for reducing peek memory in model checking. J Comput Sci Tech, 2003, 18(6): 762–770

    Article  MATH  MathSciNet  Google Scholar 

  19. Pu F, Zhang W, Wang S. An improved cased-based approach to LTL model checking. In: Proceedings of 2th International Workshop on Rapid Intergration of Software Engineering Techniques, LNCS 3943. Berlin: Springer, 2005. 190–202

    Chapter  Google Scholar 

  20. Zhang W. Model checking operator procedures. In: Proceedings of 6th International SPIN Workshop on Model Checking of Software, LNCS 1680. Berlin: Springer, 1999, 200–215

    Google Scholar 

  21. Milett L I, Teitelbaum T. Issues in slicing PROMELA and its applications to model checking, protocol understanding, and simulation. Int J Software Tools for Tech Trans, 2002, 2(4): 343–349

    Article  Google Scholar 

  22. Wu Q, Hsiao M S. A new simulation-based property checking algorithm based on partitioned alternative search space traversal. IEEE Trans Comput, 2006, 55(11): 1325–1334

    Article  Google Scholar 

  23. Huth M. Model checking modal transition systems using Kripke structures. In: Proceedings of 12th International Conference on Verification, Model Checking and Abstract Interpretation, LNCS 2294. Berlin: Springer, 2002, 302–316

    Chapter  Google Scholar 

  24. Huth M, Jagadeesan R, Schmit D. Modal transition syatems: A foundation for three-valued program analysis. In: Proceedings of European Symposium On Programming, LNCS 2028. Berlin: Springer, 2001. 155–169

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pu Fei.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 60573012 and 60421001) and the National Grand Fundamental Research 973 Program of China (Grant No. 2002cb312200)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pu, F., Zhang, W. Combining search space partition and abstraction for LTL model checking. Sci. China Ser. F-Inf. Sci. 50, 793–810 (2007). https://doi.org/10.1007/s11432-007-0073-y

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-007-0073-y

Keywords

Navigation