Statistical Model Checking of Probabilistic Frequency Temporal Logic

Abstract

Statistical model checking is approximate probabilistic model checking using statistical methods. It is originally developed for CSL whose formula has multiple probabilistic path quantifiers, however, the availability of the model checking method is limited, because it requires multiple testing. In this article, we propose an LTL-based probabilistic frequency temporal logic PFLTL whose formulae have exactly one probabilistic path quantifier, standard temporal operators, and frequency operators. A PFLTL formula can directly and intuitively express a quantitative property on a randomized behavior, with the notions of probability and frequency. Probabilistic periodicity is such a property that cannot be appropriately represented in CSL and existing real-time logics. Using statistical methods effectively, we also develop a statistical PFLTL model checking method that can check models which are untreatable in CSL model checking methods.