Reactive Proof Labeling Schemes for Distributed Decision

TL;DR

This paper extends proof labeling schemes to reactive systems, analyzing their applicability to token passing in various network topologies, and establishing existence and limitations based on network assumptions.

Contribution

It introduces reactive proof labeling schemes (RPLSs), demonstrating their existence in certain network models and proving impossibility results under specific conditions.

Findings

RPLSs exist for networks with unique identities.

RPLSs are possible for anonymous rings and general graphs.

Existence of RPLSs depends on knowledge of network size.

Abstract

We generalize the definition of Proof Labeling Schemes to reactive systems, that is, systems where the configuration is supposed to keep changing forever. As an example, we address the main classical test case of reactive tasks, namely, the task of token passing. Different RPLSs are given for the cases that the network is assumed to be a tree or an anonymous ring, or a general graph, and the sizes of RPLSs' labels are analyzed. We also address the question of whether an RPLS exists. First, on the positive side, we show that there exists an RPLS for any distributed task for a family of graphs with unique identities. For the case of anonymous networks (even for the special case of rings), interestingly, it is known that no token passing algorithm is possible even if the number n of nodes is known. Nevertheless, we show that an RPLS is possible. On the negative side, we show that if one drops the assumption that n is known, then the construction becomes impossible.