Unifying Asynchronous Logics for Hyperproperties

TL;DR

This paper introduces a new hyper logical framework, GHyperLTL_SC, unifying asynchronous extensions of HyperLTL and knowledge modalities, with a decidable model-checking fragment that can express complex properties like diagnosability and security policies.

Contribution

It defines a new expressive yet decidable fragment of hyper logic, simple GHyperLTL_SC, unifying multiple existing logics and enabling verification of complex hyperproperties.

Findings

Simple GHyperLTL_SC is more expressive than HyperLTL.

It subsumes KLTL under certain semantics.

It can express diagnosability and information-flow security policies.

Abstract

We introduce and investigate a powerful hyper logical framework in the linear-time setting, we call generalized HyperLTL with stuttering and contexts (GHyperLTL_SC for short). GHyperLTL_SC unifies known asynchronous extensions of HyperLTL 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 individuate a meaningful fragment of GHyperLTL_SC, we call simple GHyperLTL_SC, with a decidable model-checking problem, which is more expressive than HyperLTL and known fragments of asynchronous extensions of HyperLTL with a decidable model-checking problem. Simple GHyperLTL_SC 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 GHyperLTL_SC 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).