## Abstract

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 language | English |
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Pages (from-to) | 310-332 |

Number of pages | 23 |

Journal | JOURNAL OF COMPUTER AND SYSTEM SCIENCES |

Volume | 82 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Mar 2016 |

MoE publication type | A1 Journal article-refereed |

## Keywords

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