Statistical Model Checking Axel Legay 1 , Anna Lukina 2(B ) , Louis Marie Traonouez 1 , Junxing Yang 3 , Scott A. Smolka 3 , and Radu Grosu 2 1 Inria Rennes – Bretagne Atlantique, Rennes, France anna.lukina@tuwien.ac.at 2 Cyber-Physical Systems Group, Technische Universit¨at Wien, Vienna, Austria 3 Department of Computer Science, Stony Brook University, Stony Brook, USA Abstract. We highlight the contributions made in the field of Statistical Model Checking (SMC) since its inception in 2002. As the formal setting, we use a very general model of Stochastic Systems (an SS is simply a family of time-indexed random variables), and Bounded LTL (BLTL) as the temporal logic. Let S be an SS and ϕ a BLTL formula. Our survey of the area is centered around the following five main contributions. Qualitative approach to SMC: Is the probability that S satisfies ϕ greater or equal to a certain threshold? Quantitative approach to SMC: What is the probability that S satisfies ϕ? Typically this results in a confidence interval being computed for this probability. Rare Events: What happens when the probability that S satisfies ϕ is extremely small, i.e. it is a rare event? To make the SMC approach viable in this setting, rare-event estimation techniques Importance Sampling and Importance Splitting are deployed to great advantage. Optimal Planning: Motivated by the success of Importance Sampling and Importance Splitting in rare-event SMC, we explore the use of these techniques in the context of optimal planning. In particu- lar, we consider ARES, an optimal-planning approach based on a notion of adaptive receding-horizon planning. We illustrate the util- ity of ARES on the planning problem of bringing a flock of birds (autonomous agents) from a random initial configuration to a V- formation, an energy-conservation formation deployed by migrating geese. Somewhat ironically, the performance of ARES can be evalu- ated using (quantitative) SMC, as the problem to be solved is of the form F (J ≤ θ); i.e. does an ARES-generated plan eventually bring the flock to a configuration where the flock-wide cost function J is below a given threshold θ? Optimal Control: We show that the techniques we presented for optimal planning in the form of ARES carry over to the control setting in the form of Adaptive-Horizon Model-Predictive Control (AMPC). We again use the V-formation problem for evaluation purposes. We also introduce the concept of V-formation games, and show how the power of AMPC can be used to ward off cyber-physical attacks. c  Springer Nature Switzerland AG 2019 B. Steffen and G. Woeginger (Eds.): Computing and Software Science, LNCS 10000, pp. 478–504, 2019. https://doi.org/10.1007/978-3-319-91908-9_23