Temporal logic for properties with relative frequency

Abstract

Inherently unreliable or fault-tolerant systems demand for a specification formalism that allows the user to express a required ratio of certain observations. Such a requirement can be, e.g. that deadlines in a real-time system must be met in at least 80% of all cases. Logics and in particular temporal logics provide powerful, flexible and well established specification formalisms. We therefore propose fLTL, an extension to linear-time temporal logic that allows for expressing relative frequencies by an intuitive generalization of the temporal operators. We develop a game theoretical methodology and a semantics for temporal logic with counters. For our novel logic, we establish an undecidability result regarding the satisfiability problem but identify a decidable fragment which strictly increases the expressiveness of linear-time temporal logic by allowing, e.g., to express non-context-free properties.