@article{DolevHJKLRSW:JCSS2016, title = {Synchronous Counting and Computational Algorithm Design}, author = {Danny Dolev and Keijo Heljanko and Matti J\"arvisalo and Janne H. Korhonen and Christoph Lenzen and Joel Rybicki and Jukka Suomela and Siert Wieringa}, journal = {Journal of Computer and System Sciences}, volume = {82}, number = {2}, pages = {310--332}, year = {2016}, } 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.