{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T12:18:43Z","timestamp":1778069923286,"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":[[2026,3,17]]},"abstract":"<jats:p>Motivated by the theory of proof complexity generators we consider the following $\u03a3^p_2$ search problem $\\mbox{DD}_P$ determined by a propositional proof system $P$: given a $P$-proof $\u03c0$ of a disjunction $\\bigvee_i \u03b1_i$, no two $\u03b1_i$ having an atom in common, find $i$ such that $\u03b1_i \\in \\mbox{TAUT}$. We formulate a hypothesis (ST) that for some strong proof system $P$ the problem $\\mbox{DD}_P$ is not solvable in the student-teacher model with a $p$-time student and a constant number of rounds. The hypothesis follows from the existence of hard one-way permutations. We prove, using a model-theoretic assumption, that (ST) implies $NP \\neq coNP$. The assumption concerns the existence of extensions of models of a bounded arithmetic theory and it is open at present if it holds.<\/jats:p>","DOI":"10.46298\/lmcs-22(2:14)2026","type":"journal-article","created":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T11:45:12Z","timestamp":1778067912000},"source":"Crossref","is-referenced-by-count":0,"title":["On $NP \\cap coNP$ proof complexity generators"],"prefix":"10.46298","volume":"Volume 22, Issue 2","author":[{"given":"Jan","family":"Krajicek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2026,5,6]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/arXiv:2506.20221v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/arXiv:2506.20221v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T11:45:12Z","timestamp":1778067912000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/15980"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,6]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-22(2:14)2026","relation":{"has-preprint":[{"id-type":"arxiv","id":"arXiv:2506.20221v3","asserted-by":"subject"},{"id-type":"arxiv","id":"arXiv:2506.20221v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2506.20221","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.arXiv:2506.20221","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,6]]},"article-number":"15980"}}