  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.
