2026-07-24T11:55:05Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6229 2024-03-06T10:37:50Z ddc:004 open_access

Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness Chen, Hubie proof complexity polynomial hierarchy quantified propositional logic We present and study a framework in which one can present alternation-based lower bounds on proof length in proof systems for quantified Boolean formulas. A key notion in this framework is that of proof system ensemble, which is (essentially) a sequence of proof systems where, for each, proof checking can be performed in the polynomial hierarchy. We introduce a proof system ensemble called relaxing QU-res which is based on the established proof system QU-resolution. Our main results include an exponential separation of the tree-like and general versions of relaxing QU-res, and an exponential lower bound for relaxing QU-res; these are analogs of classical results in propositional proof complexity. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hubie Chen 2016 Is Part Of LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2016.94 urn:nbn:de:0030-drops-62290 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.94 eng https://creativecommons.org/licenses/by/3.0/legalcode