Model Checking HyperRecHML is Decidable

Abstract

Temporal hyperlogics combine explicit quantification over traces with temporal requirements evaluated over the quantified traces. HyperRecHML is a temporal hyperlogic which allows for arbitrary mixing of trace quantification and the use of fixed points for expressing temporal requirements, which makes it very expressive in comparison to other first-order hyperlogics. HyperRecHML has already been successfully applied in runtime verification, but the decidability of its model checking problem remains open. We answer this question positively by providing two main contributions. Firstly, a normalization procedure that allows to reduce arbitrary HyperRecHML formulas to a normal form with restricted nesting of trace quantification and fixed points. Secondly, we provide an automata-based model checking algorithm for formulas of this normal form. The complexity of our algorithm is comparable to similar ones for other hyperlogics, despite the extra expressive power.