  Distributed fault-tolerance can mask the effect of a limited number of
permanent faults, while self-stabilization provides forward recovery after an
arbitrary number of transient fault hit the system. FTSS protocols combine the
best of both worlds since they are simultaneously fault-tolerant and
self-stabilizing. To date, FTSS solutions either consider static (i.e. fixed
point) tasks, or assume synchronous scheduling of the system components. In
this paper, we present the first study of dynamic tasks in asynchronous
systems, considering the unison problem as a benchmark. Unison can be seen as a
local clock synchronization problem as neighbors must maintain digital clocks
at most one time unit away from each other, and increment their own clock value
infinitely often. We present many impossibility results for this difficult
problem and propose a FTSS solution when the problem is solvable that exhibits
optimal fault containment.
