Uniform Monte-Carlo Model Checking

Abstract

Abstract. 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 Büchi 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.

Statistical Model Checking for Variability-Intensive Systems

“…First, we seek for guaranteeing the absence of bugs in all variants of the family (applying family-based concepts), while they focus on dynamic feature interactions (on a product-based basis). The second difference is that they consider quantitative bounded properties, while we support the entire LTL verification problem by extending the multi-lasso concept of [20,28].…”

“…A motivated criticism [28] of the use of random walk to sample lasso is that shorter lassos receive a higher probability to be sampled. To counterbalance this, we implemented a heuristic named multi-lasso [20].…”

Uniform Sampling for Timed Automata with Application to Language Inclusion Measurement

“…Monte Carlo or statistical model checking usually employs an isotropic random walk to explore the executions (as explained in [19,11] for discrete models). This involves choosing uniformly at random, at each step of the simulation, the next transition from those available.…”

Counting for Random Testing

“…In [18], we have studied how to perform uniform random generation of lassos, which are the kind of paths of interest for LTL model-checking. This implies counting and drawing elementary circuits, which is known as a hard problem.…”

“…This paper is organised as follows: Section 2 recalls some basic facts on software random testing and random walks; Section 3 briefly presents methods for uniform generation of bounded paths that are completely described in [17] and [5]; Section 4 shows how to take into account other coverage criteria, and gives a definition of randomised coverage satisfaction [5] ; finally Section 5 addresses the uniform coverage of lassos, which are the basis of LTL model-checking [18].…”