Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties

TL;DR

This paper investigates the expressiveness and decidability of temporal logics for asynchronous hyperproperties, comparing their expressive power, analyzing singleton models, and establishing new decidability boundaries for model checking.

Contribution

It provides a comprehensive comparison of asynchronous hyperproperty logics, characterizes singleton models, and identifies new decidability results for HyperLTL_C.

Findings

Almost complete expressiveness characterization of these logics.

Undecidability of singleton model existence for two asynchronous extensions.

New decidability boundaries for model checking HyperLTL_C.

Abstract

Hyperproperties are properties of systems that relate different executions traces, with many applications from security to symmetry, consistency models of concurrency, etc. In recent years, different linear-time logics for specifying asynchronous hyperproperties have been investigated. Though model checking of these logics is undecidable, useful decidable fragments have been identified with applications e.g. for asynchronous security analysis. In this paper, we address expressiveness and decidability issues of temporal logics for asynchronous hyperproperties. We compare the expressiveness of these logics together with the extension S1S[E] of S1S with the equal-level predicate by obtaining an almost complete expressiveness picture. We also study the expressive power of these logics when interpreted on singleton sets of traces. We show that for two asynchronous extensions of HyperLTL, checking the existence of a singleton model is already undecidable, and for one of them, namely Context HyperLTL (HyperLTL_C), we establish a characterization of the singleton models in terms of the extension of standard FO[<] over traces with addition. This last result generalizes the well-known equivalence between FO[<] and LTL. Finally, we identify new boundaries on the decidability of model checking HyperLTL_C.