The Worst-Case Stabilization Time of a Self-Stabilizing Algorithm under the Weakly Fair Daemon Model

In this paper, the result of any self-stabilizing algorithm under the weakly fair daemon model (for a particular problem) that is not self-stabilizing under the non-fair central daemon model is obtained. Also, if any safe configuration under the weakly fair daemon model is also a safe configuration under the non-fair central daemon model, the worst-case stabilization time, measured in steps, is infinity. The implication of this new finding is that any problem, the existence of self-stabilizing algorithms for the weakly fair daemon model only, is unsatisfactory, that is of significance to pursue self-stabilizing algorithms for the non-fair central daemon model.