mit-licenseDolev, DannyKorhonen, Janne H.Lenzen, ChristophRybicki, JoelSuomela, Jukka2025-03-242013-04-212013-04-21https://hydatakatalogi-test-24.it.helsinki.fi/handle/123456789/9417Consider a complete communication network on n nodes, each of which is a state machine with s states. 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”. We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates f Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states s. We use computational techniques to construct very compact deterministic algorithms for the first non-trivial case of f = 1. While no algorithm exists for n < 4, we show that as few as 3 states are sufficient for all values n ≥ 4. We prove that the problem cannot be solved with only 2 states for n = 4, but there is a 2-state solution for all values n ≥ 6. This repository contains: computer-generated algorithms, computer-generated lower-bound proofs, Python scripts that can be used to verify that the algorithms and the lower-bound proofs are correct, additional illustrations. For more information, see: doi:10.1007/978-3-319-03089-0_17 arXiv:1304.5719Opensoftware