文章基本信息

标题：Parameterized Valiant's Classes
本地全文：下载
作者：Markus Bl{"a}ser ; Christian Engels
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：148
页码：1-14
DOI：10.4230/LIPIcs.IPEC.2019.3
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We define a theory of parameterized algebraic complexity classes in analogy to parameterized Boolean counting classes. We define the classes VFPT and VW[t], which mirror the Boolean counting classes #FPT and #W[t], and define appropriate reductions and completeness notions. Our main contribution is the VW[1]-completeness proof of the parameterized clique family. This proof is far more complicated than in the Boolean world. It requires some new concepts like composition theorems for bounded exponential sums and Boolean-arithmetic formulas. In addition, we also look at two polynomials linked to the permanent with vastly different parameterized complexity.
关键词：Algebraic complexity theory; parameterized complexity theory; Valiant's classes