{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:24Z","timestamp":1753894404390,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>The Merge Resolution proof system (M-Res) for QBFs, proposed by Beyersdorff\net al. in 2019, explicitly builds partial strategies inside refutations. The\noriginal motivation for this approach was to overcome the limitations\nencountered in long-distance Q-Resolution proof system (LD-Q-Res), where the\nsyntactic side-conditions, while prohibiting all unsound resolutions, also end\nup prohibiting some sound resolutions. However, while the advantage of M-Res\nover many other resolution-based QBF proof systems was already demonstrated, a\ncomparison with LD-Q-Res itself had remained open. In this paper, we settle\nthis question. We show that M-Res has an exponential advantage over not only\nLD-Q-Res, but even over LQU$^+$-Res and IRM, the most powerful among currently\nknown resolution-based QBF proof systems. Combining this with results from\nBeyersdorff et al. 2020, we conclude that M-Res is incomparable with LQU-Res\nand LQU$^+$-Res. Our proof method reveals two additional and curious features\nabout M-Res: (i) M-Res is not closed under restrictions, and is hence not a\nnatural proof system, and (ii) weakening axiom clauses with existential\nvariables provably yields an exponential advantage over M-Res without\nweakening. We further show that in the context of regular derivations,\nweakening axiom clauses with universal variables provably yields an exponential\nadvantage over M-Res without weakening. These results suggest that M-Res is\nbetter used with weakening, though whether M-Res with weakening is closed under\nrestrictions remains open. We note that even with weakening, M-Res continues to\nbe simulated by eFrege $+$ $\\forall$red (the simulation of ordinary M-Res was\nshown recently by Chew and Slivovsky).<\/jats:p>","DOI":"10.46298\/lmcs-20(3:22)2024","type":"journal-article","created":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T07:55:09Z","timestamp":1725954909000},"source":"Crossref","is-referenced-by-count":0,"title":["QBF Merge Resolution is powerful but unnatural"],"prefix":"10.46298","volume":"Volume 20, Issue 3","author":[{"given":"Meena","family":"Mahajan","sequence":"first","affiliation":[]},{"given":"Gaurav","family":"Sood","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,9,10]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/14232\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/14232\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T07:55:09Z","timestamp":1725954909000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/12710"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,10]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(3:22)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2205.13428v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2205.13428v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2205.13428","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2205.13428","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,9,10]]},"article-number":"12710"}}