Approximate Verification of Probabilistic Systems

Abstract

General methods have been proposed [2,4] for the model checking of probabilistic systems, where the verification of a probabilistic statement is reduced to the solution of a linear system over the system’s state space. To overcome the state space explosion problem, some probabilistic model checkers, such as PRISM [3], use MTBDDs. We propose a different solution, in which we use a Monte-Carlo algorithm [6] to approximate Prob[ψ], the probability that a temporal formula is true. We show how to obtain a randomized estimator of Prob[ψ] for a fragment of LTL formulas. This fragment is sufficient to express interesting properties such as reachability and liveness.