Abstract
The verification process of reactive systems in local model checking [2,9,28] and in explicit state model checking [14,16] is on-the-fly. Therefore only those states of a system have to be traversed that are necessary to prove a property. In addition, if the property does not hold, than often only a small subset of the state space has to be traversed to produce a counterexample. Global model checking [8,24] and, in particular, symbolic model checking [6,23] can utilize compact representations of the state space, e.g. BDDs [5], to handle much larger designs than what is possible with local and explicit model checking. We present a new model checking algorithm for LTL that combines both approaches. In essence, it is a generalization of the tableau construction of [2] that enables the use of BDDs but still is onthefly.
This research is sponsored by the Semiconductor Research Corporation (SRC) under Contract No. 98-DJ-294, and the National Science Foundation (NSF) under Grant No. CCR-9505472. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of SRC, NSF, or the United States Government.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
I. Beer, S. Ben-David, C. Eisner, D. Geist, L. Gluhovsky, T. Heyman, A. Landver, P. Paanah, Y. Rodeh, G. Ronin, and Y. Wolfsthal. Rulebase: Model checking at IBM. In CVA‘97, number 1254 in LNCS, pages 480–483. Springer-Verlag, 1997.
G. Bhat, R. Cleaveland, and O. Grumberg. Efficient on-the-fly model checking for CTL*. In LICS‘95. IEEE Computer Society, 1995.
A. Biere, A. Cimatti, E. Clarke, and Y. Zhu. Symbolic model checking without BDDs. In TACAS‘99, LNCS. Springer, 1999.
J. Bradfield and C. Stirling. Local model checking for infinite state spaces. Theorectical Computer Science, 96:157–174, 1992.
R. E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers, 35(8), 1986.
J. R. Burch, E. M. Clarke, and K. L. McMillan. Symbolic model checking: 1020 states and beyond. Information and Computation, 98, 1992.
E. Clarke, O. Grumberg, and K. Hamaguchi. Another look at LTL model checking.Formal Methods in System Design, 10:47–71, 1997.
E. M. Clarke and E. A. Emerson. Design and synthesis of synchronization skeletons using branching time temporal logic. In Logic of Programs: Workshop, LNCS. Springer, 1981.
R. Cleaveland. Tableau-based model checking in the propositional mu-calculus. Acta Informatica, 27, 1990.
M. Dam. CTL*and ECTL* as fragments of the modal mu-calculus. Theoretical Computer Science, 126, 1994.
D. L. Dill. The MurΦ verification system. In CAV‘96, LNCS. Springer, 1996.
Y. Dong, X. Du, Y.S. Ramakrishna, C. T. Ramkrishnan, I. V. Ramakrishnan, S. A. Smolka, O. Sokolsky, E. W. Starck, and D. S. Warren. Fighting livelock in the i-protocol: tiA comparative study of verification tools. In TACAS‘99, LNCS. Springer, 1999.
E. A. Emerson and C.-L. Lei. Modalities for model checking: Branching time strikes back. Science of Computer Programming, 8, 1986.
R. Gerth, D. Peled, M. Y. Vardi, and P. Wolper. Simple on-the-fly automatic verification of linear temporal logic. In Proceedings 15th Workshop on Protocol Specification, Testing, and Verification. North-Holland, 1995.
T. A. Henzinger, O. Kupferman, and S. Qadeer. From Pre-historic to Post-modern symbolic model checking. In CAV‘98, LNCS. Springer, 1998.
G. J. Holzmann. The model checker SPIN. IEEE Transactions on Software Engineering, 5(23) 1997.
H. Iwashita and T. Nakata. CTL model checking based on forward state traversal. In ICCAD‘96. ACM, 1996.
H. Iwashita, T. Nakata, and F. Hirose. Forward model checking techniques oriented to buggy design. In ICCAD‘97. ACM, 1997.
A. Kick. Generierung von Gegenbeispielen und Zeugen bei der Modellprüfung. PhD thesis, Fakultät für Informatik, Universität Karlsruhe, 1996.
D. Kozen. Results on the propositional µ-calculus. Theoretical Computer Science, 27, 1983.
O. Lichtenstein and A. Pnueli. Checking that finite state concurrent programs satisfy their linear specification. In Symposium on Principles of Programming Languages, New York, 1985. ACM.
D. E. Long, A. Browne, E. M. Clarke, S. Jha, and W. R. Marrero. An improved algorithm for the evaluation of fixpoint expressions. In CAV‘94, LNCS. Springer, 1994.
K. L. McMillan. Symbolic Model Checking. Kluwer, 1993.
J. P. Quielle and J. Sifakis. Specification and verification of concurrent systems in CESAR. In Proc. 5th Int. Symp. in Programming, 1981.
K. Ravi, K. L. McMillan, T. R. Shiple, and F. Somenzi. Approximation and decomposition of binary decision diagrams. In DAC‘98. ACM, 1998.
K. Ravi and F. Somenzi. High-density reachability analysis. In ICCAD‘95. ACM, 1995.
F. Reffel. Modellprüfung von Unterlogiken von CTL*. Masterthesis, Fakultät für Informatik, Universität Karlsruhe, 1996.
C. Stirling and D. Walker. Local model checking in the modal mu-calculus. Theoretical Computer Science, 89, 1991.
M. Y. Vardi and P. Wolper. Reasoning about infinite computations. Information and Computation, 115(1), 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Biere, A., Zhu, Y., Clarke, E.M. (1999). Multiple State and Single State Tableaux for Combining Local and Global Nodel Checking. In: Olderog, ER., Steffen, B. (eds) Correct System Design. Lecture Notes in Computer Science, vol 1710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48092-7_8
Download citation
DOI: https://doi.org/10.1007/3-540-48092-7_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66624-0
Online ISBN: 978-3-540-48092-1
eBook Packages: Springer Book Archive