Approximate Agreement under Mobile Byzantine Faults

TL;DR

This paper introduces a new approach to approximate agreement in mobile Byzantine fault models by mapping them to mixed-mode faults, establishing lower bounds, and proposing matching upper bounds, advancing understanding of fault-tolerant distributed algorithms.

Contribution

It presents the first mapping from Mobile Byzantine models to Mixed-Mode faults, proves lower bounds for these models, and provides matching upper bounds for approximate agreement.

Findings

Mapping from Mobile Byzantine to Mixed-Mode faults established

Lower bounds for Mobile Byzantine models proved

Matching upper bounds for approximate agreement proposed

Abstract

In this paper we address Approximate Agreement problem in the Mobile Byzantine faults model. Our contribution is threefold. First, we propose the the first mapping from the existing variants of Mobile Byzantine models to the Mixed-Mode faults model.This mapping further help us to prove the correctness of class MSR (Mean-Subsequence-Reduce) Approximate Agreement algorithms in the Mobile Byzantine fault model, and is of independent interest. Secondly, we prove lower bounds for solving Approximate Agreement under all existing Mobile Byzantine faults models. Interestingly, these lower bounds are different from the static bounds. Finally, we propose matching upper bounds. Our paper is the first to link the Mobile Byzantine Faults models and the Mixed-Mode Faults models, and we advocate that a similar approach can be adopted in order to prove the correctness of other classical distributed building blocks (e.g. agreement, clock synchronization, interactive consistency etc) under Mobile Byzantine Faults model.