An effective heuristic for adaptive importance splitting in statistical model checking

Abstract

Statistical model checking avoids the intractable growth of states associated with numerical model checking by estimating the probability of a property from simulations. Rare properties pose a challenge because the relative error of the estimate is unbounded. In [13] we describe how importance splitting may be used with SMC to overcome this problem. The basic idea is to decompose a logical property into nested properties whose probabilities are easier to estimate. To improve performance it is desirable to decompose the property into many equiprobable levels, but logical decomposition alone may be too coarse. In this article we make use of the notion of a score function to improve the granularity of a logical property. We show that such a score function may take advantage of heuristics, so long as it also rigorously respects certain properties. To demonstrate our importance splitting approach we present an optimal adaptive importance splitting algorithm and an heuristic score function. We give experimental results that demonstrate a significant improvement in performance over alternative approaches.