Abstract
In this paper, we present a complete bounded model checking algorithm for the universal fragment of μ-calculus. The new algorithm checks the completeness of bounded proof of each property on the fly and does not depend on prior knowledge of the completeness thresholds. The key is to combine both local and bounded model checking techniques and use SAT solvers to perform local model checking on finite Kripke structures. Our proof-theoretic approach works for any property in the specification logic and is more general than previous work on specific properties. We report experimental results to compare our algorithm with the conventional BDD-based algorithm.
This work was supported in part by NSC grand NSC 93-2213-E-001-012-.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without bDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)
Biere, A., Cimatti, A., Clarke, E.M., Fujita, M., Zhu, Y.: Symbolic model check- ing using SAT procedures instead of BDDs. In: Proceedings of the 36th Design Automation Conference (DAC 1999), pp. 317–320. ACM Press, New York (1999)
Emerson, E., Clarke, E.: Using branching-time temporal logic to synthesize syn- chronization skeletons. Science of Computer Programming 2, 241–266 (1982)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (1999)
Clarke, E., Kröning, D., Ouaknine, J., Strichman, O.: Completeness and complexity of bounded model checking. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 85–96. Springer, Heidelberg (2004)
Sheeran, M., Singh, S., Stålmarck, 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)
de Moura, L., Rueß, H., Sorea, M.: Bounded model checking and induction: From refutation to verification. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 14–26. Springer, Heidelberg (2003)
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)
Awedh, M., Somenzi, F.: Proving more properties with bounded model checking. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 96–108. Springer, Heidelberg (2004)
Emerson, E.A., Lei, C.L.: Eficient model-checking in fragments of the propositional mu-calculus. In: Proceedings First Annual IEEE Symposium on Logic in Computer Science, pp. 267–278. IEEE Computer Society Press, Los Alamitos (1986)
Vardi, M., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proceedings First Annual IEEE Symposium on Logic in Computer Science, pp. 332–344. IEEE Computer Society Press, Los Alamitos (1986)
Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond. Information and Computation 98, 142–170 (1992)
Cleaveland, R.: Tableau-based model checking in the propositional mu-calculus. Acta Informatica 27, 725–747 (1989)
Stirling, C., Walker, D.: Local model checking in the modal mu-calculus. Theoretical Computer Science 89, 161–177 (1991)
Andersen, H.R., Stirling, C., Winskel, G.: A compositional proof system for the modal μ-calculus. In: Proceedings, Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France, pp. 144–153. IEEE Computer Society Press, Los Alamitos (1994)
Emerson, E., Lei, C.: Modalities for model-checking: Branching time logic strikes back. In: Proceedings of the 12th ACM Symposium on Principles of Programming Languages, pp. 84–96. ACM Press, New York (1985)
Schuppan, V., Biere, A.: Eficient reduction of finite state model checking to reachability analysis. Software Tools for Technology Transfer 5, 185–204 (2004)
Schuele, T., Schneider, K.: Global vs. local model checking: A comparison of verification techniques for infinite state systems. In: International Conference on Soft- ware Engineering and Formal Methods (SEFM), Beijing. IEEE Computer Society Press, Los Alamitos (2004)
Schuele, T., Schneider, K.: Bounded local model checking. Private communication (2005)
Wang, B.Y.: Unbounded model checking with sat - a local model checking approach. unpublished manuscript (2004)
Kozen, D.: Results on the propositional μ-calculus. Theoretical Computer Science 27, 333–354 (1983)
Winskel, G.: A note on model checking the modal nu-calculus. Theoretical Computer Science 83, 157–167 (1991)
Wang, B.Y.: Proving ∀ μ-calculus properties with sat-based model checking. Technical Report TR-IIS-05-003, Institute of Information Science, Academia Sinica (2005), http://www.iis.sinica.edu.tw/LIB/TechReport/tr2005/tr05003.pdf
Clarke, E., Grumberg, O., Hamaguchi, K.: Another look at LTL model checking. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 415–428. Springer, Heidelberg (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 IFIP International Federation for Information Processing
About this paper
Cite this paper
Wang, BY. (2005). Proving ∀μ-Calculus Properties with SAT-Based Model Checking. In: Wang, F. (eds) Formal Techniques for Networked and Distributed Systems - FORTE 2005. FORTE 2005. Lecture Notes in Computer Science, vol 3731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11562436_10
Download citation
DOI: https://doi.org/10.1007/11562436_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29189-3
Online ISBN: 978-3-540-32084-5
eBook Packages: Computer ScienceComputer Science (R0)