2026-07-23T16:35:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14204 2024-03-06T10:53:44Z ddc:004 open_access

Kernelization, Proof Complexity and Social Choice Istrate, Gabriel Bonchiş, Cosmin Crăciun, Adrian Kernelization Frege proofs Kneser-Lovász Theorem Arrow’s theorem Gibbard-Satterthwaite theorem We display an application of the notions of kernelization and data reduction from parameterized complexity to proof complexity: Specifically, we show that the existence of data reduction rules for a parameterized problem having (a). a small-length reduction chain, and (b). small-size (extended) Frege proofs certifying the soundness of reduction steps implies the existence of subexponential size (extended) Frege proofs for propositional formalizations of the given problem. We apply our result to infer the existence of subexponential Frege and extended Frege proofs for a variety of problems. Improving earlier results of Aisenberg et al. (ICALP 2015), we show that propositional formulas expressing (a stronger form of) the Kneser-Lovász Theorem have quasipolynomial size Frege proofs for each constant value of the parameter k. Another notable application of our framework is to impossibility results in computational social choice: we show that, for any fixed number of agents, propositional translations of the Arrow and Gibbard-Satterthwaite impossibility theorems have subexponential size Frege proofs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Gabriel Istrate and Cosmin Bonchiş and Adrian Crăciun 2021 Is Part Of LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2021.135 urn:nbn:de:0030-drops-142043 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.135 eng https://creativecommons.org/licenses/by/4.0/legalcode