On Approximate Probabilistic Model Checking of Unbounded Until Properties

We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with state-space explosion that makes the model checking process practically inefficient for large systems. However, the existing methods consider a restricted subset of PCTL, specifically, the subset that can only express bounded until properties. We propose a new method that does not rely on such restriction and can be effectively used to reason about unbounded until properties. We approximate probabilistic characteristics of an unbounded until property by that of a bounded until property for suitably chosen value of the bound. In essence, our method is a two-phase process; the first phase is concerned with identifying the bound k0, while the second phase applies standard statistical methods for verifying k0-bounded until properties. We empirically show the practical applicability of our method using a research prototype implementation by verification of finitebuffer queue (M/M/1/K) and dining philosopher problems modeled as Discrete Time Markov Chains against properties expressed in Probabilistic Computational Tree Temporal Logic (PCTL).