Abstract
-
Probabilistic model checking is a verification technique that has been the focus of intensive research for over a decade. One
important issue with probabilistic model checking, which is crucial for its practical significance but is overlooked by the state-of-the-art
largely, is the potential discrepancy between a stochastic model and the real-world system it represents when the model is built from
statistical data. In the worst case, a tiny but nontrivial change to some model quantities might lead to misleading or even invalid
verification results. To address this issue, in this paper, we present a mathematical characterization of the consequences of model
perturbations on the verification distance. The formal model that we adopt is a parametric variant of discrete-time Markov chains
equipped with a vector norm to measure the perturbation. Our main technical contributions include a closed-form formulation of
asymptotic perturbation bounds, and computational methods for two arguably most useful forms of those bounds, namely linear
bounds and quadratic bounds. We focus on verification of reachability properties but also address automata-based verification of
omega-regular properties. We present the results of a selection of case studies that demonstrate that asymptotic perturbation bounds
can accurately estimate maximum variations of verification results induced by model perturbations.