Unifying Asynchronous Logics for Hyperproperties

Abstract

We introduce and investigate a powerful hyper logical framework in the linear-time setting that we call generalized HLTL with stuttering and contexts (GHLTL for short). GHLTL unifies the asynchronous extensions of HLTL called SHLTL and CHLTL, and the well-known extension KLTL of LTL with knowledge modalities under both the synchronous and asynchronous perfect recall semantics. As a main contribution, we identify a meaningful fragment of GHLTL, that we call simple GHLTL, with a decidable model-checking problem, which is more expressive than HLTL and known fragments of asynchronous extensions of HLTL with a decidable model-checking problem. Simple GHLTL subsumes KLTL under the synchronous semantics and the one-agent fragment of KLTL under the asynchronous semantics and to the best of our knowledge, it represents the unique hyper logic with a decidable model-checking problem which can express powerful non-regular trace properties when interpreted on singleton sets of traces. We justify the relevance of simple GHLTL by showing that it can express diagnosability properties, interesting classes of information-flow security policies, both in the synchronous and asynchronous settings, and bounded termination (more in general, global promptness in the style of Prompt LTL).