  Self-stabilization is a strong property that guarantees that a network always
resume correct behavior starting from an arbitrary initial state. Weaker
guarantees have later been introduced to cope with impossibility results:
probabilistic stabilization only gives probabilistic convergence to a correct
behavior. Also, weak stabilization only gives the possibility of convergence.
In this paper, we investigate the relative power of weak, self, and
probabilistic stabilization, with respect to the set of problems that can be
solved. We formally prove that in that sense, weak stabilization is strictly
stronger that self-stabilization. Also, we refine previous results on weak
stabilization to prove that, for practical schedule instances, a deterministic
weak-stabilizing protocol can be turned into a probabilistic self-stabilizing
one. This latter result hints at more practical use of weak-stabilization, as
such algorthms are easier to design and prove than their (probabilistic)
self-stabilizing counterparts.
