Towards Optimal Synchronous Counting

TL;DR

This paper introduces new deterministic algorithms for synchronous counting in networks with Byzantine faults, achieving linear stabilization time, minimal state usage, and near-optimal resilience, representing a significant improvement over prior randomized or resource-intensive methods.

Contribution

The authors present deterministic algorithms for synchronous counting that are space-efficient, have linear stabilization time, and nearly optimal fault tolerance, improving upon previous approaches.

Findings

Deterministic algorithms with linear stabilization time.

Reduced state complexity compared to prior methods.

Achieved near-optimal resilience against Byzantine faults.

Abstract

Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is to eventually have all correct nodes counting modulo $c$ in agreement. Thus, we are considering algorithms that are self-stabilizing despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have linear stabilisation time in $f$, (3) use a small number of states, and (4) achieve almost-optimal resilience. Prior algorithms either resort to randomisation, use a large number of states, or have poor resilience. In particular, we achieve an exponential improvement in the space complexity of deterministic algorithms, while still achieving linear stabilisation time and almost-linear resilience.