{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T02:55:40Z","timestamp":1777776940493,"version":"3.51.4"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2026,2,15]]},"abstract":"<jats:p>We study the existence of positional strategies for the protagonist in infinite duration games over arbitrary game graphs. We prove that prefix-independent objectives in $\u03a3_0^2$ which are positional and admit a (strongly) neutral letter are exactly those that are recognised by history-deterministic monotone co-Bchi automata over countable ordinals. This generalises a criterion proposed by [Kopczy\u0144ski, ICALP 2006] and gives an alternative proof of closure under union for these objectives, which was known from [Ohlmann, TheoretiCS 2023].   We then give two applications of our result. First, we prove that the mean-payoff objective is positional over arbitrary game graphs. Second, we establish the following completeness result: for any objective $W$ which is prefix-independent, admits a (weakly) neutral letter, and is positional over finite game graphs, there is an objective $W'$ which is equivalent to $W$ over finite game graphs and positional over arbitrary game graphs.<\/jats:p>","DOI":"10.46298\/lmcs-22(2:10)2026","type":"journal-article","created":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T18:40:07Z","timestamp":1777488007000},"source":"Crossref","is-referenced-by-count":0,"title":["Positionality in $\u03a3_0^2$ and a completeness result"],"prefix":"10.46298","volume":"Volume 22, Issue 2","author":[{"given":"Pierre","family":"Ohlmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Micha\u0142","family":"Skrzypczak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2026,4,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2309.17022v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2309.17022v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T18:40:07Z","timestamp":1777488007000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/14054"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-22(2:10)2026","relation":{"has-preprint":[{"id-type":"arxiv","id":"2309.17022v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2309.17022v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2309.17022","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2309.17022","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,29]]},"article-number":"14054"}}