Asynchronous Extensions of HyperLTL

TL;DR

This paper introduces two asynchronous extensions of HyperLTL, expanding its expressiveness for asynchronous hyperproperties, and identifies decidable fragments with known complexity, advancing formal verification methods.

Contribution

The paper proposes HyperLTLS and HyperLTLC, two asynchronous extensions of HyperLTL, and characterizes their decidable fragments and computational complexity.

Findings

Model checking for the extensions is generally undecidable.

Decidable fragments subsume HyperLTL and are practically expressive.

HyperLTLS fragment has the same complexity as HyperLTL.

Abstract

Hyperproperties are a modern specification paradigm that extends trace properties to express properties of sets of traces. Temporal logics for hyperproperties studied in the literature, including HyperLTL, assume a synchronous semantics and enjoy a decidable model checking problem. In this paper, we introduce two asynchronous and orthogonal extensions of HyperLTL, namely Stuttering HyperLTL (HyperLTLS) and Context HyperLTL (HyperLTLC). Both of these extensions are useful, for instance, to formulate asynchronous variants of information-flow security properties. We show that for these logics, model checking is in general undecidable. On the positive side, for each of them, we identify a fragment with a decidable model checking that subsumes HyperLTL and that can express meaningful asynchronous requirements. Moreover, we provide the exact computational complexity of model checking for these two fragments which, for the HyperLTLS fragment, coincides with that of the strictly less expressive logic HyperLTL.