Synchronous counting and computational algorithm design

Research output: Contribution to journalArticle


  • Danny Dolev
  • Keijo Heljanko
  • Matti Järvisalo
  • Janne Korhonen
  • Christoph Lenzen
  • Joel Rybicki
  • Jukka Suomela

  • Siert Wieringa

Research units

  • Hebrew University of Jerusalem
  • University of Helsinki
  • MPI for Informatics


Consider a complete communication network on n nodes. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". Furthermore, the solution needs to be self-stabilising (reaching correct operation from any initial state) and tolerate f Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms either require a source of random bits or a large number of states per node. In this work, we give fast state-optimal deterministic algorithms for the first non-trivial case f=1. To obtain these algorithms, we develop and evaluate two different techniques for algorithm synthesis. Both are based on casting the synthesis problem as a propositional satisfiability (SAT) problem; a direct encoding is efficient for synthesising time-optimal algorithms, while an approach based on counter-example guided abstraction refinement discovers non-optimal algorithms quickly.


Original languageEnglish
Pages (from-to)310-332
Number of pages23
Issue number2
Publication statusPublished - 1 Mar 2016
MoE publication typeA1 Journal article-refereed

    Research areas

  • Byzantine fault tolerance, Distributed computing, Formal methods, SAT, Self-stabilisation, Synthesis

ID: 1564084