Silent Anonymous Snap-Stabilizing Termination Detection

Abstract

We address the problem of Termination Detection (TD) in asynchronous networks. It is known that TD cannot be achieved in the context of self-stabilization, except in the specific case where the TD algorithm is snap-stabilizing, i.e., it always behaves according to its specification regardless of the initial configuration. In this paper, we propose a generic, deterministic, snap-stabilizing, silent algorithm that detects whether an observed terminating silent self-stabilizing algorithm, A, has converged to a configuration that satisfies an intended predicate. Our algorithm assumes that nodes know (an upper bound on) the network diameter D. However, it requires no underlying structure, nor specific topology (arbitrary network), and works in anonymous networks, i.e., our algorithm uses no kind of assumption allowing distinguishing one or more nodes. Furthermore, it works under the weakest scheduling assumptions a.k.a, the unfair daemon. Built over any asynchronous self-stabilizing underlying unison U, our solution adds only O(log D) bits per node. Since there exists no unison algorithm with better space complexity, the extra space of our solution is negligible w.r.t. the space complexity of the underlying unison algorithm. Our algorithm provides a positive answer in O(max (k, k’, D)) time units, where k and k’ are the stabilization time complexities of A and U, respectively.