{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:40:56Z","timestamp":1753890056706,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T00:00:00Z","timestamp":1511827200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T00:00:00Z","timestamp":1511827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T00:00:00Z","timestamp":1511827200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-16-CE40-0023"],"award-info":[{"award-number":["ANR-16-CE40-0023"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-16-CE25-0009"],"award-info":[{"award-number":["ANR-16-CE25-0009"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We propose a general framework to build certified proofs of distributed self-stabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model in the self-stabilizing area. We then validate our framework by certifying a non trivial part of an existing silent self-stabilizing algorithm which builds a $k$-clustering of the network. We also certify a quantitative property related to the output of this algorithm. Precisely, we show that the computed $k$-clustering contains at most $\\lfloor \\frac{n-1}{k+1} \\rfloor + 1$ clusterheads, where $n$ is the number of nodes in the network. To obtain these results, we also developed a library which contains general tools related to potential functions and cardinality of sets.<\/jats:p>","DOI":"10.23638\/lmcs-13(4:14)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:11Z","timestamp":1743701291000},"source":"Crossref","is-referenced-by-count":1,"title":["A Framework for Certified Self-Stabilization"],"prefix":"10.23638","volume":"Volume 13, Issue 4","author":[{"given":"Karine","family":"Altisen","sequence":"first","affiliation":[]},{"given":"Pierre","family":"Corbineau","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8032-9732","authenticated-orcid":false,"given":"Stephane","family":"Devismes","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,11,28]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1610.08685v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1610.08685v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:12Z","timestamp":1743701292000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2183"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,28]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(4:14)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1610.08685v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1610.08685v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1610.08685","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1610.08685","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,11,28]]},"article-number":"2183"}}