On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

TL;DR

This paper explores the computational capabilities of Population Protocols under unreliable and weaker interaction models, introducing omission failures and one-way communication, and presents simulators that enable two-way protocols to operate in these constrained settings.

Contribution

It introduces omission failures in Population Protocols and develops simulators that enable two-way protocols to function under weaker, one-way, and failure-prone interaction models.

Findings

Omission failures can be detected or undetected, affecting protocol design.

Simulators can convert two-way protocols into one-way or failure-prone models.

We establish conditions under which weaker models can simulate standard two-way protocols.

Abstract

In this paper we investigate the computational power of Population Protocols (PP) under some unreliable and/or weaker interaction models. More precisely, we focus on two features related to the power of interactions: omission failures and one-way communications. An omission failure, a notion that this paper introduces for the first time in the context of PP, is the loss by one or both parties of the information transmitted in an interaction. The failure may or may not be detected by either party. On the other hand, in one-way models, communication happens only in one direction: only one of the two agents can change its state depending on both agents' states, and the other agent may or may not be aware of the interaction. These notions can be combined, obtaining one-way protocols with (possibly detectable) omission failures. A general question is what additional power is necessary and sufficient to completely overcome the weakness of one-way protocols and enable them to simulate two-way protocols, with and without omission failures. As a basic feature, a simulator needs to implement an atomic communication of states between two agents; this task is further complicated by the anonymity of the agents, their lack of knowledge of the system, and the limited amount of memory that they may have. We provide the first answers to these questions by presenting and analyzing several simulators, i.e., wrapper protocols converting any protocol for the standard two-way model into one running on a weaker one.