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

Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties