[{"oa":1,"abstract":[{"lang":"eng","text":"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."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"fulldoi":"https://doi.org/10.1007/s00446-018-0342-6","date_created":"2018-12-11T11:44:30Z","day":"12","scopus_import":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","language":[{"iso":"eng"}],"publication_status":"published","publist_id":"7978","type":"journal_article","file_date_updated":"2020-07-14T12:48:01Z","department":[{"_id":"DaAl"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["000"],"date_published":"2018-09-12T00:00:00Z","has_accepted_license":"1","file":[{"access_level":"open_access","date_created":"2018-12-17T14:21:22Z","content_type":"application/pdf","file_id":"5711","relation":"main_file","file_name":"2018_DistributedComputing_Lenzen.pdf","file_size":799337,"date_updated":"2020-07-14T12:48:01Z","creator":"dernst","checksum":"872db70bba9b401500abe3c6ae2f1a61"}],"oa_version":"Published Version","publication":"Distributed Computing","license":"https://creativecommons.org/licenses/by/4.0/","isi":1,"citation":{"short":"C. Lenzen, J. Rybicki, Distributed Computing (2018).","ieee":"C. Lenzen and J. Rybicki, “Near-optimal self-stabilising counting and firing squads,” <i>Distributed Computing</i>. Springer, 2018.","apa":"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>","mla":"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>.","ista":"Lenzen C, Rybicki J. 2018. Near-optimal self-stabilising counting and firing squads. Distributed Computing.","ama":"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>","chicago":"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>."},"publisher":"Springer","author":[{"full_name":"Lenzen, Christoph","first_name":"Christoph","last_name":"Lenzen"},{"first_name":"Joel","last_name":"Rybicki","id":"334EFD2E-F248-11E8-B48F-1D18A9856A87","full_name":"Rybicki, Joel","orcid":"0000-0002-6432-6646"}],"date_updated":"2025-04-15T06:53:15Z","status":"public","year":"2018","corr_author":"1","title":"Near-optimal self-stabilising counting and firing squads","external_id":{"isi":["000475627800005"]},"_id":"76","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00446-018-0342-6","month":"09"}]