article published yes Christoph Lenzen author Joel Rybicki author 334EFD2E-F248-11E8-B48F-1D18A9856A870000-0002-6432-6646 DaAl department IST Austria Open Access Fund project Consider a fully-connected synchronous distributed system consisting of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous C-counting problem, all nodes need to eventually agree on a counter that is increased by one modulo C in each round for given C&gt;1. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external “go” signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a “fire” signal. Moreover, no node should generate a “fire” signal without some correct node having previously received a “go” signal as input. We present a framework reducing both tasks to binary consensus at very small cost. For example, we obtain a deterministic algorithm for self-stabilising Byzantine firing squads with optimal resilience f&lt;n/3, asymptotically optimal stabilisation and response time O(f), and message size O(log f). As our framework does not restrict the type of consensus routines used, we also obtain efficient randomised solutions. https://research-explorer.ista.ac.at/download/76/5711/2018_DistributedComputing_Lenzen.pdf application/pdfno Springer2018 eng 00047562780000510.1007/s00446-018-0342-6 Lenzen, Christoph, and Joel Rybicki. “Near-Optimal Self-Stabilising Counting and Firing Squads.” <i>Distributed Computing</i>. Springer, 2018. <a href="https://doi.org/10.1007/s00446-018-0342-6">https://doi.org/10.1007/s00446-018-0342-6</a>. Lenzen, C., &#38; Rybicki, J. (2018). Near-optimal self-stabilising counting and firing squads. <i>Distributed Computing</i>. Springer. <a href="https://doi.org/10.1007/s00446-018-0342-6">https://doi.org/10.1007/s00446-018-0342-6</a> C. Lenzen and J. Rybicki, “Near-optimal self-stabilising counting and firing squads,” <i>Distributed Computing</i>. Springer, 2018. Lenzen, Christoph, and Joel Rybicki. “Near-Optimal Self-Stabilising Counting and Firing Squads.” <i>Distributed Computing</i>, Springer, 2018, doi:<a href="https://doi.org/10.1007/s00446-018-0342-6">10.1007/s00446-018-0342-6</a>. Lenzen C, Rybicki J. Near-optimal self-stabilising counting and firing squads. <i>Distributed Computing</i>. 2018. doi:<a href="https://doi.org/10.1007/s00446-018-0342-6">10.1007/s00446-018-0342-6</a> C. Lenzen, J. Rybicki, Distributed Computing (2018). Lenzen C, Rybicki J. 2018. Near-optimal self-stabilising counting and firing squads. Distributed Computing. 762018-12-11T11:44:30Z2025-04-15T06:53:15Z