  Failure detectors are oracles that have been introduced to provide processes
in asynchronous systems with information about faults. This information can
then be used to solve problems otherwise unsolvable in asynchronous systems. A
natural question is on the "minimum amount of information" a failure detector
has to provide for a given problem. This question is classically addressed
using a relation that states that a failure detector D is stronger (that is,
provides "more, or better, information") than a failure detector D' if D can be
used to implement D'. It has recently been shown that this classic
implementability relation has some drawbacks. To overcome this, different
relations have been defined, one of which states that a failure detector D is
stronger than D' if D can solve all the time-free problems solvable by D'. In
this paper we compare the implementability-based hierarchy of failure detectors
to the hierarchy based on solvability. This is done by introducing a new proof
technique for establishing the solvability relation. We apply this technique to
known failure detectors from the literature and demonstrate significant
differences between the hierarchies.
