{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T14:15:55Z","timestamp":1754144155286,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,16]]},"abstract":"<jats:p>We show that the big-O problem for max-plus automata is decidable and PSPACE-complete. The big-O (or affine domination) problem asks whether, given two max-plus automata computing functions f and g, there exists a constant c such that f &amp;lt; cg+ c. This is a relaxation of the containment problem asking whether f &amp;lt; g, which is undecidable. Our decidability result uses Simon's forest factorisation theorem, and relies on detecting specific elements, that we call witnesses, in a finite semigroup closed under two special operations: stabilisation and flattening.<\/jats:p>","DOI":"10.46298\/lmcs-21(3:3)2025","type":"journal-article","created":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T08:00:08Z","timestamp":1752566408000},"source":"Crossref","is-referenced-by-count":0,"title":["The Big-O Problem for Max-Plus Automata is Decidable (PSPACE-Complete)"],"prefix":"10.46298","volume":"Volume 21, Issue 3","author":[{"given":"Laure","family":"Daviaud","sequence":"first","affiliation":[]},{"given":"David","family":"Purser","sequence":"additional","affiliation":[]},{"given":"Marie","family":"Tcheng","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,7,15]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2304.05229v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2304.05229v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T08:00:08Z","timestamp":1752566408000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/13539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,15]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(3:3)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2304.05229v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2304.05229v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2304.05229","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2304.05229","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,7,15]]},"article-number":"13539"}}