Frequency Linear-time Temporal Logic

We propose fLTL, an extension to linear-time temporal logic (LTL) that allows for expressing relative frequencies by a generalization of temporal operators. This facilitates the specification of requirements such as the deadlines in a realtime system must be met in at least 95% of all cases. For our novel logic, we establish an undecidability result regarding the satisfiability problem but identify a decidable fragment which strictly increases the expressiveness of LTL by allowing, e.g., to express non-context-free properties.