Immediate Observation in Mediated Population Protocols

TL;DR

This paper investigates the computational capabilities of mediated population protocols under immediate observation constraints, showing they are at least as powerful as basic population protocols and exploring their potential equivalence to mediated protocols.

Contribution

It introduces a novel configuration notion and translation techniques demonstrating the computational power of IOMPP, a restricted mediated population protocol model.

Findings

IOMPP is at least as powerful as basic population protocols.

A generic translation preserves protocol properties.

Potential equivalence of IOMPP and MPP models is conjectured.

Abstract

In this paper we analyze the computational power of variants of population protocols (PP), a formalism for distributed systems with anonymous agents having very limited capabilities. The capabilities of agents are enhanced in mediated population protocols (MPP) by recording the states in the edges of the interaction graph. Restricting the interactions to the communication model of immediate observation (IO) reduces the computational power of the resulting formalism. We show that this enhancement and restriction, when combined, yield a model (IOMPP) at least as powerful as the basic PP. The proof requires a novel notion of configurations in the MPP model allowing differentiation of agents and uses techniques similar to methods of analyzing encoding criteria, namely operational correspondence. The constructional part of the proof is generic in a way that all protocols can be translated into the new model without losing the desirable properties they might have besides a stable output. Furthermore, we illustrate how this approach could be utilized to prove our conjecture of IOMPP model being even as expressive as the MPP model. If our conjecture holds, this would result in a sharp characterization of the computational power and reveal the nonnecessity of two-way communication in the context of mediated population protocols.