Clopper-Pearson Algorithms for Efficient Statistical Model Checking Estimation

Statistical model checking (SMC) is a simulation-based formal verification technique to deal with the scalability problem faced by traditional model checking. The main workflow of SMC is to perform iterative simulations. The number of simulations depends on users’ requirement for the verification results, which can be very large if users require a high level of confidence and precision. Therefore, how to perform as fewer simulations as possible while achieving the same level of confidence and precision is one of the core problems of SMC. In this paper, we consider the estimation problem of SMC. Most existing statistical model checkers use the Okamoto bound to decide the simulation number. Although the Okamoto bound is sound, it is well known to be overly conservative. The simulation number decided by the Okamoto bound is usually much higher than it actually needs, which leads to a waste of time and computation resources. To tackle this problem, we propose an efficient, sound and lightweight estimation algorithm using the Clopper-Pearson confidence interval. We perform comprehensive numerical experiments and case studies to evaluate the performance of our algorithm, and the results show that our algorithm uses 40%-60% fewer simulations than the Okamoto bound. Our algorithm can be directly integrated into existing model checkers to reduce the verification time of SMC estimation problems.