New Insights on p-safety of Stochastic Systems

The concept of p-safety is a specialization of the stochastic reach-avoidance problem with probability threshold constraints in a barrier certificate manner for stochastic processes. All in all, the objective of p-safety is to identify the set of initial states, from which the probability to reach an unsafe region before reaching a desired target, is small enough (less then p). Identification of the set of these initial states is the core of the safety problem. In this paper, we develop further the theory of p-safety focusing on mathematical characterizations and approximation methods for the associated p-safety function and measure.