2026-07-23T07:16:13Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:5716 2024-03-06T10:36:55Z ddc:004 open_access

Are Short Proofs Narrow? QBF Resolution is not Simple Beyersdorff, Olaf Chew, Leroy Mahajan, Meena Shukla, Anil proof complexity QBF resolution lower bound techniques simulations The groundbreaking paper 'Short proofs are narrow - resolution made simple' by Ben-Sasson and Wigderson (J. ACM 2001) introduces what is today arguably the main technique to obtain resolution lower bounds: to show a lower bound for the width of proofs. Another important measure for resolution is space, and in their fundamental work, Atserias and Dalmau (J. Comput. Syst. Sci. 2008) show that space lower bounds again can be obtained via width lower bounds. Here we assess whether similar techniques are effective for resolution calculi for quantified Boolean formulas (QBF). A mixed picture emerges. Our main results show that both the relations between size and width as well as between space and width drastically fail in Q-resolution, even in its weaker tree-like version. On the other hand, we obtain positive results for the expansion-based resolution systems Forall-Exp+Res and IR-calc, however only in the weak tree-like models. Technically, our negative results rely on showing width lower bounds together with simultaneous upper bounds for size and space. For our positive results we exhibit space and width-preserving simulations between QBF resolution calculi. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Olaf Beyersdorff and Leroy Chew and Meena Mahajan and Anil Shukla 2016 Is Part Of LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2016.15 urn:nbn:de:0030-drops-57164 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.15 eng https://creativecommons.org/licenses/by/3.0/legalcode