2026-07-24T05:11:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11464 2024-03-06T10:48:05Z ddc:004 open_access

Parameterized Valiant’s Classes Bläser, Markus Engels, Christian Algebraic complexity theory parameterized complexity theory Valiant’s classes 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Markus Bläser and Christian Engels 2019 Is Part Of LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2019.3 urn:nbn:de:0030-drops-114648 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.3 eng https://creativecommons.org/licenses/by/3.0/legalcode