Unifying Hyper and Epistemic Temporal Logics

In the literature, two powerful temporal logic formalisms have been proposed for expressing information-flow security requirements, that in general, go beyond regular properties. One is classic, based on the knowledge modalities of epistemic logic. The other one, the so-called hyper logic, is more recent and subsumes many proposals from the literature. In an attempt to better understand how these logics compare with each other, we consider the logic KCTL∗ (the extension of CTL∗ with knowledge modalities and synchronous perfect recall semantics) and HyperCTL∗. We first establish that KCTL∗ and HyperCTL∗ are expressively incomparable. Then, we introduce a natural linear past extension of HyperCTL∗, called HyperCTLlp, that unifies KCTL ∗ and HyperCTL∗. We show that the model-checking problem for HyperCTLlp is decidable, and we provide its exact computational complexity in terms of a new measure of path quantifiers’ alternation. For this, we settle open complexity issues for unrestricted quantified propositional temporal logic.