# Towards optimal synchronous counting

PODC 2015 · 34th Annual ACM Symposium on Principles of Distributed Computing, Donostia-San Sebastián, Spain, July 2015 ·

# Abstract

Consider a complete communication network of $n$ nodes, in which 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 count modulo $c$ in agreement. Thus, we are considering algorithms that are self-stabilising 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 state complexity of deterministic algorithms, while still achieving linear stabilisation time and almost-linear resilience.

# Publication

Chryssis Georgiou and Paul G. Spirakis (Eds.): PODC’15, Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, July 21–23, 2015, Donostia–San Sebastián, Spain, pages 441–450, ACM Press, New York, 2015

ISBN 978-1-4503-3617-8

# Journal Version

© ACM 2015 — This is the authors’ version of the work. It is posted here for your personal use. Not for redistribution. The definitive version was published in Proc. PODC 2015.

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