Completeness and complexity of bounded model checking

Edmund Clarke, Daniel Kroening, Joël Ouaknine, and Ofer Strichman

For every finite model M and LTL property φ, there exists a number CT (the Completeness Threshold) such that if there is no counterexample to φ in M of length CT or less, then M satisfies φ. Finding this number, if it is sufficiently small, offers a practical method for making Bounded Model Checking complete. We describe how to compute an over-approximation to CT for a general LTL property using Büchi automata, following the Vardi-Wolper LTL model checking framework. Based on the value of CT, we prove that the complexity of standard SAT-based BMC is doubly exponential, and that consequently there is a complexity gap of an exponent between this procedure and standard LTL model checking. We discuss ways to bridge this gap.

The article mainly focuses on observations regarding bounded model checking rather than on a presentation of new techniques.

Proceedings of VMCAI 04, LNCS 2937, 2004. 12 pages.

PostScript / PDF © 2004 Springer-Verlag.

Note: This paper is superceded by
E. M. Clarke, D. Kroening, J. Ouaknine, and O. Strichman. Computational challenges in bounded model checking. International Journal on Software Tools for Technology Transfer 7(2), 2005.

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