Expected Constant Time Self-stabilizing Byzantine Pulse Resynchronization

TL;DR

This paper introduces a novel approach for Byzantine pulse resynchronization that guarantees expected constant time stabilization from arbitrary states, improving efficiency and flexibility over existing solutions.

Contribution

It presents a new geometric framework integrating agreement and random walk techniques, enabling optimal expected stabilization time without requiring regular pulse generation.

Findings

Expected constant time stabilization achieved

Reduced message complexity compared to prior solutions

Can convert irregular pulses into synchronized pulses efficiently

Abstract

In extending fast digital clock synchronization to the bounded-delay model, the expected constant time Byzantine pulse resynchronization problem is investigated. In this problem, the synchronized state of the system should not only be deterministically maintained but be reached from arbitrary states with expected constant time in the presence of Byzantine faults. An intuitive geometric representation of the problem is introduced, with which the classical approximate agreement, randomized Byzantine agreement, and random walk are integrated with some geometric operations. Efficient realizations are also provided for practical uses. Compared with the state-of-the-art solutions, the assumed common pulses need not be regularly generated, the message complexity can be lowered as approximate agreement, and the expected stabilization time is optimal. With this, the provided solution can efficiently convert irregularly generated common pulses to self-stabilizing Byzantine pulse synchronization.