Uniform Monte-Carlo Model Checking

Grosu and Smolka have proposed a randomised Monte-Carlo algorithm for LTL model-checking. Their method is based on random exploration of the intersection of the model and of the Buchi automaton that represents the property to be checked. The targets of this exploration are so-called lassos, i.e. elementary paths followed by elementary circuits. During this exploration outgoing transitions are chosen uniformly at random. Grosu and Smolka note that, depending on the topology, the uniform choice of outgoing transitions may lead to very low probabilities of some lassos. In such cases, very big numbers of random walks are required to reach an acceptable coverage of lassos, and thus a good probability either of satisfaction of the property or of discovery of a counter-example. In this paper, we propose an alternative sampling strategy for lassos in the line of the uniform exploration of models presented in some previous work. The problem of finding all elementary cycles in a directed graph is known to be difficult: there is no hope for a polynomial time algorithm. Therefore, we consider a well-known sub-class of directed graphs, namely the reducible flow graphs, which correspond to well-structured programs and most control-command systems. We propose an efficient algorithm for counting and generating uniformly lassos in reducible flowgraphs. This algorithm has been implemented and experimented on a pathological example. We compare the lasso coverages obtained with our new uniform method and with uniform choice among the outgoing transitions.