{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:27Z","timestamp":1753894407466,"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":[[2025,3,11]]},"abstract":"<jats:p>We investigate the proof complexity of systems based on positive branching programs, i.e. non-deterministic branching programs (NBPs) where, for any 0-transition between two nodes, there is also a 1-transition. Positive NBPs compute monotone Boolean functions, just like negation-free circuits or formulas, but constitute a positive version of (non-uniform) NL, rather than P or NC1, respectively.   The proof complexity of NBPs was investigated in previous work by Buss, Das and Knop, using extension variables to represent the dag-structure, over a language of (non-deterministic) decision trees, yielding the system eLNDT. Our system eLNDT+ is obtained by restricting their systems to a positive syntax, similarly to how the 'monotone sequent calculus' MLK is obtained from the usual sequent calculus LK by restricting to negation-free formulas.   Our main result is that eLNDT+ polynomially simulates eLNDT over positive sequents. Our proof method is inspired by a similar result for MLK by Atserias, Galesi and Pudl\\'ak, that was recently improved to a bona fide polynomial simulation via works of Je\\v{r}\\'abek and Buss, Kabanets, Kolokolova and Kouck\\'y. Along the way we formalise several properties of counting functions within eLNDT+ by polynomial-size proofs and, as a case study, give explicit polynomial-size poofs of the propositional pigeonhole principle.<\/jats:p>","DOI":"10.46298\/lmcs-21(1:23)2025","type":"journal-article","created":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T08:40:11Z","timestamp":1741682411000},"source":"Crossref","is-referenced-by-count":0,"title":["Proof complexity of positive branching programs"],"prefix":"10.46298","volume":"Volume 21, Issue 1","author":[{"given":"Anupam","family":"Das","sequence":"first","affiliation":[]},{"given":"Avgerinos","family":"Delkos","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,3,11]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/15354\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/15354\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T08:40:11Z","timestamp":1741682411000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/13874"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,11]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(1:23)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2102.06673v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2102.06673v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2102.06673","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2102.06673","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,3,11]]},"article-number":"13874"}}