How to pass from local to global scales in anonymous networks? How to organize a selfstabilizing propagation of information with feedback. From the Angluin impossibility results, we cannot elect a leader in a general anonymous network. Thus, it is impossible to build a rooted spanning tree. Many problems can only be solved by probabilistic methods. In this paper we show how to use Unison to design a self-stabilizing barrier synchronization in an anonymous network. We show that the commuication structure of this barrier synchronization designs a self-stabilizing wave-stream, or pipelining wave, in anonymous networks. We introduce two variants of Wave: the strong waves and the wavelets. A strong wave can be used to solve the idempotent r-operator parametrized computation problem. A wavelet deals with k-distance computation. We show how to use Unison to design a self-stabilizing wave stream, a self-stabilizing strong wave stream and a self-stabilizing wavelet stream.
We show how fault-tolerance can be effectively added to several types of faults in program computations that use barrier synchronization. We divide the faults that occur in practice into two classes, detectable and undetectable, and design a fully distributed program that tolerates the faults in both classes. Our program guarantees that every barrier is executed correctly even if detectable faults occur, and that eventually every barrier is executed correctly even if undetectable faults occur. Via analytical as well as simulation results we show that the cost of adding fault-tolerance is low, in part by comparing the times required by our program with that required by the corresponding fault-intolerant counterpart. Synchronization of ABD networks assertional verification distributed infimum approximation garbage collection.