Sequential schemes for frequentist estimation of properties in statistical model checking

Statistical Model Checking (SMC) is an approximate verification method that overcomes the state space explosion problem for probabilistic systems by Monte Carlo simulations. Simulations might be however costly if many samples are required. It is thus necessary to implement efficient algorithms to reduce the sample size while preserving precision and accuracy. In the literature, some sequential schemes have been provided for the estimation of property occurrence based on predefined confidence and absolute or relative error. Nevertheless, these algorithms remain conservative and may result in huge sample sizes if the required precision standards are demanding. In this article, we compare some useful bounds and some sequential methods based on frequentist estimations. We propose outperforming and rigorous alternative schemes, based on Massart bounds and robust confidence intervals. Our theoretical and empirical analysis show that our proposal reduces the sample size while providing guarantees on error bounds.