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-Lov\'asz Theorem have polynomial size Frege proofs for each constant value of the parameter k. Previously only quasipolynomial bounds were known (and only for the ordinary Kneser-Lov\'asz Theorem). 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.

翻译：我们展示了从参数复杂性到证明复杂性的内分泌和数据减少概念的应用:具体地说,我们展示了存在数据减少规则的参数化问题有(a)小减量链和(b)小尺寸(延伸)的折叠证明,证明削减步骤的健全性,意味着存在参数k的每个不变值的亚爆炸性大小(延伸)断层证明(延伸) 。我们应用了我们的结果,推断存在一系列问题的亚爆炸性裂变和扩展的裂变证明。改进了Aisenberg 等人(ECRIP 2015)的早期结果,我们展示了表达(一种较强形式的)Kneser-Lov\'as Theorem的公式,表示参数 k. 的每个不变值都有聚度尺寸的折变体证明。以前只知道准极离子表面界限(只有普通的Kneser-Lov\'as Theorem ) 。我们框架的另一个显著应用是无法实现计算性社会选择的结果:我们展示了任何固定的箭状号的箭状号的变体规模。