Abstract
Partial Kripke structures model incomplete state spaces with unknown parts. The evaluation of temporal logic formulae on partial Kripke structures is thus based on three-valued interpretations; the additional truth value \(\bot\) stands for “unknown whether property true or false”. There are existing model checking algorithms as well as tools employing this three-valued interpretation.
In this paper we study the applicability of bounded model checking techniques to partial Kripke structures. To this end, we generalise the translation of Kripke structure and temporal logic formula to propositional logic as to include the value \(\bot\), and define a new notion of satisfiability for propositional formulae containing \(\bot\) as constants. We show that a check for this kind of satisfiability can be reduced to two checks for ordinary two-valued satisfiability, thus allowing for the use of standard SAT solvers.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andrade, J.O., Yonezawa, T.: Multi-valued bounded model checking. Technical report, Department of Computer Science, University of Tsukuba, Japan (2004)
Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Advances in Computers 58, 118–149 (2003)
Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic Model Checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)
Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic Model Checking: 1020 States and Beyond. Inf. Comput. 98(2), 142–170 (1992)
Bruns, G., Godefroid, P.: Model checking partial state spaces with 3-valued temporal logics. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 274–287. Springer, Heidelberg (1999)
Bruns, G., Godefroid, P.: Generalized Model Checking: Reasoning about Partial State Spaces. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 168–182. Springer, Heidelberg (2000)
Chechik, M., Devereux, B., Easterbrook, S.M., Gurfinkel, A.: Multi-valued symbolic model-checking. ACM Trans. Softw. Eng. Methodol. 12(4), 371–408 (2003)
Chechik, M., Easterbrook, S.M., Devereux, B.: Model checking with multi-valued temporal logics. In: ISMVL, pp. 187–192 (2001)
Clarke, E., Grumberg, O., Peled, D.: Model checking. MIT Press, Cambridge (1999)
Fitting, M.: Kleene’s three valued logics and their children. Fundam. Inform. 20(1/2/3), 113–131 (1994)
Gurfinkel, A., Chechik, M.: Multi-valued model checking via classical model checking. In: Amadio, R., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 263–277. Springer, Heidelberg (2003)
Gurfinkel, A., Chechik, M.: Why waste a perfectly good abstraction? In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 212–226. Springer, Heidelberg (2006)
Kramer, J., Magee, J.: Self-Managed Systems: an Architectural Challenge. In: ICSE 2007 - Future of Software Engineering Track. ACM Press, New York (2007)
Konikowska, B., Penczek, W.: Reducing Model Checking from Multi-valued CTL* to CTL*. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 226–239. Springer, Heidelberg (2002)
Liu, C., Kuehlmann, A., Moskewicz, M.: CAMA: A Multi-Valued Satisfiability Solver. In: International Conference on Computer Aided Design, pp. 326–333. IEEE/ACM (November 2003)
Larsen, K.G., Thomsen, B.: A modal process logic. In: LICS, pp. 203–210. IEEE Computer Society, Los Alamitos (1988)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: DAC, pp. 530–535. ACM, New York (2001)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, Heidelberg (1992)
Prasad, M.R., Biere, A., Gupta, A.: A survey of recent advances in SAT-based formal verification. STTT 7(2), 156–173 (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wehrheim, H. (2008). Bounded Model Checking for Partial Kripke Structures. In: Fitzgerald, J.S., Haxthausen, A.E., Yenigun, H. (eds) Theoretical Aspects of Computing - ICTAC 2008. ICTAC 2008. Lecture Notes in Computer Science, vol 5160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85762-4_26
Download citation
DOI: https://doi.org/10.1007/978-3-540-85762-4_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85761-7
Online ISBN: 978-3-540-85762-4
eBook Packages: Computer ScienceComputer Science (R0)