Abstract
This work presents game-based model checking for abstract models with respect to specifications in μ-calculus, interpreted over a 3-valued semantics. If the model checking result is indefinite (don’t know), the abstract model is refined, based on an analysis of the cause for this result. For finite concrete models our abstraction-refinement is fully automatic and guaranteed to terminate with a definite result true or false.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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(2), 142–170 (1992)
Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855. Springer, Heidelberg (2000)
Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT press, Cambridge (1999)
Clarke, E., 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, p. 265. Springer, Heidelberg (2002)
Cleaveland, R.: Tableau-based model checking in the propositional mu-calculus. Acta Inf. 27, 725–747 (1990)
Dams, D., Gerth, R., Grumberg, O.: Abstract interpretation of reactive systems. ACM Transactions on Programming Languages and Systems 19(2) (March 1997)
Emerson, E.A., Jutla, C.S.: Tree automata, μ-calculus and determinacy. In: Proc. 32th Symp. on Foundations of Computer Science (FOCS 1991), pp. 368–377. IEEE Computer Society Press, Los Alamitos (1991)
Emerson, E.A., Lei, C.-L.: Efficient model checking in fragments of the propositional mu-calculus. In: Logic in Computer Science, LICS (1986)
Godefroid, P., Jagadeesan, R.: Automatic abstraction using generalized model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 137–150. Springer, Heidelberg (2002)
Godefroid, P., Jagadeesan, R.: On the expressiveness of 3-valued models. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 206–222. Springer, Heidelberg (2002)
Huth, M., Jagadeesan, R., Schmidt, D.: Modal transition systems: A foundation for three-valued program analysis. In: Sands, D. (ed.) ESOP 2001. LNCS, vol. 2028, pp. 155–169. Springer, Heidelberg (2001)
Kozen, D.: Results on the Propositional μ-calculus. TCS 27, 333–354 (1983)
Lee, W., Pardo, A., Jang, J.-Y., Hachtel, G.D., Somenzi, F.: Tearing based automatic abstraction for CTL model checking. In: ICCAD, pp. 76–81 (1996)
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)
Long, D., Browne, A., Clark, E., Jha, S., Marrero, W.: An improved algorithm for the evaluation of fixpoint expressions. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 338–350. Springer, Heidelberg (1994)
Pardo, A., Hachtel, G.D.: Automatic abstraction techniques for propositional mu-calculus model checking. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254. Springer, Heidelberg (1997)
Pardo, A., Hachtel, G.D.: Incremental CTL model checking using BDD subsetting. In: Design Automation Conference (DAC), pp. 457–462 (1998)
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)
Stirling, C.: Local model checking games. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 1–11. Springer, Heidelberg (1995)
Stirling, C., Walker, D.J.: Local model checking in the modal mu-calculus. In: Díaz, J., Orejas, F. (eds.) TAPSOFT 1989 and CCIPL 1989. LNCS, vol. 352. Springer, Heidelberg (1989)
Tarski, A.: A lattice-theoretical fixpoint theorem and its application. Pacific J.Math. 5, 285–309 (1955)
Winskel, G.: Model checking in the modal ν-calculus. In: International Colloquium on Automata, Languages, and Programming, ICALP (1989)
Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoretical Computer Science 200(1–2), 135–183 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Grumberg, O., Lange, M., Leucker, M., Shoham, S. (2005). Don’t Know in the μ-Calculus. In: Cousot, R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2005. Lecture Notes in Computer Science, vol 3385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30579-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-30579-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24297-0
Online ISBN: 978-3-540-30579-8
eBook Packages: Computer ScienceComputer Science (R0)