Machine-based methods in parameterized complexity theory

Authors:
Yijia Chen;Jörg Flum;Martin Grohe
Affiliations:
Intitute für Informatik, Humboldt-Universität zu Berlin, Berlin, Germany;Abteilung für Mathematische Logik, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany;Intitute für Informatik, Humboldt-Universität zu Berlin, Berlin, Germany
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

We give machine characterizations of most parameterized complexity classes, in particular, of W[P], of the classes of the W-hierarchy, and of the A-hierarchy. For example, we characterize W[P] as the class of all parameterized problems decidable by a nondeterministic fixed-parameter tractable algorithm whose number of nondeterministic steps is bounded in terms of the parameter. The machine characterizations suggest the introduction of a hierarchy Wfunc between the W- and the A-hierarchy. We study the basic properties of this hierarchy.