Abstract
For two naturals m,n such that m < n, we show how to construct a circuit C with m inputs and n outputs, that has the following property: for some 0 ≤ k ≤ m, the circuit defines a k-universal function. This means, informally, that for every subset K of k outputs, every possible valuation of the variables in K is reachable (we prove that k is very close to m with an arbitrarily high probability). Now consider a circuit M with n inputs that we wish to model-check. Connecting the inputs of M to the outputs of C gives us a new circuit M′ with m inputs, that its original inputs have freedom defined by k. This is a very attractive feature for underapproximation in model-checking: on one hand the combined circuit has a smaller number of inputs, and on the other hand it is expected to find an error state fast if there is one.
We report initial experimental results with bounded model checking of industrial designs (the method is equally applicable to unbounded model checking and to simulation), which shows mixed results. An interesting observation, however, is that in 13 out of 17 designs, setting m to be n/5 is sufficient to detect the bug. This is in contrast to other underapproximation that are based on reducing the number of inputs, which in most cases cannot detect the bug even with m = n/2.
Chapter PDF
Similar content being viewed by others
References
Amla, N., McMillan, K.: Automatic abstraction without counterexamples. In: Garavel, H., Hatcliff, J. (eds.) ETAPS 2003 and TACAS 2003. LNCS, vol. 2619, Springer, Heidelberg (2003)
Barner, S., Grumberg, O.: Combining symmetry reduction and upper-approximation for symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, Springer, Heidelberg (2002)
Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. J. ACM 50(5), 752–794 (2003)
Clarke, E., Gupta, A., Strichman, O.: SAT based counterexample-guided abstraction-refinement. Transactions on Computer Aided Design (TCAD) 23(7), 1113–1123 (2004)
Glusman, M., Kamhi, G., Mador-Haim, S., Fraer, R., Vardi, M.Y.: Multiple-counterexample guided iterative abstraction refinement: An industrial evaluation. In: Garavel, H., Hatcliff, J. (eds.) ETAPS 2003 and TACAS 2003. LNCS, vol. 2619, pp. 176–191. Springer, Heidelberg (2003)
Grumberg, O., Lerda, F., Strichman, O., Theobald, M.: Proof-guided underapproximation-widening for multi-process systems. In: POPL 2005. Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 122–131. ACM Press, New York (2005)
Hartman, A., Raskin, L.: Problems and algorithms for covering arrays. Discrete Math. 284, 149–156 (2004)
Kurshan, R.: Computer aided verification of coordinating processes. Princeton University Press, Princeton, NJ (1994)
Nisan, N., Wigderson, A.: Hardness vs randomness. Journal of Computer and System Sciences 49, 146–167 (1994)
Ravi, K., Somenzi, F.: High-density reachability analysis. In: Proc. Intl. Conf. on Computer-Aided Design, pp. 154–158 (November 1995)
Ravi, K., Somenzi, F.: Hints to accelerate symbolic traversal. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 250–264. Springer, Heidelberg (1999)
Seroussi, G., Bshouty, N.: Vector sets for exhaustive testing of logic circuits. IEEE Transactions on Information Theory, 34 (1988)
Williams, R., Gomes, C.P., Selman, B.: Backdoors to typical case complexity. In: IJCAI, pp. 1173–1178 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Matsliah, A., Strichman, O. (2007). Underapproximation for Model-Checking Based on Random Cryptographic Constructions. In: Damm, W., Hermanns, H. (eds) Computer Aided Verification. CAV 2007. Lecture Notes in Computer Science, vol 4590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73368-3_39
Download citation
DOI: https://doi.org/10.1007/978-3-540-73368-3_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73367-6
Online ISBN: 978-3-540-73368-3
eBook Packages: Computer ScienceComputer Science (R0)