An Asymptotically Correct Finite Path Semantics for LTL

Runtime verification of temporal logic properties requires a definition of the truth value of these properties on the finite paths that are observed at runtime. However, while the semantics of temporal logic on infinite paths has been precisely defined, there is not yet an agreement on the definition of the semantics on finite paths. Recently, it has been observed that the accuracy of runtime verification can be improved by a 4-valued semantics of temporal logic on finite paths. However, as we argue in this paper, even a 4-valued semantics is not sufficient to achieve a semantics on finite paths that converges to the semantics on infinite paths. To overcome this deficiency, we consider in this paper Manna and Pnueli’s temporal logic hierarchy consisting of safety, liveness (guarantee), co-Büchi (persistence), and Büchi (recurrence) properties. We propose the use of specialized semantics for each of these subclasses to improve the accuracy of runtime verification. In particular, we prove that our new semantics converges to the infinite path semantics which is an important property that has not been achieved by previous approaches.