| |
VOLUME 1, ISSUE 1, PAPER 2
|
Model-checking problems as a basis for parameterized intractability
|
©Jörg Flum, Mathematisches Institut, Universität Freiburg
©Martin Grohe, Institut für Informatik, Humboldt-Universität zu Berlin
|
Abstract
Most parameterized complexity classes are defined in terms of a
parameterized version of the Boolean satisfiability problem (the
so-called weighted satisfiability problem). For example, Downey and
Fellow's W-hierarchy is of this form. But there are also classes, for example,
the A-hierarchy, that are more naturally characterised in terms of
model-checking problems for certain fragments of first-order logic.
Downey, Fellows, and Regan (1998) were the first to establish a
connection between the two formalisms by giving a characterisation of the
W-hierarchy in terms of first-order model-checking problems. We improve their result and then prove a similar correspondence between weighted
satisfiability and model-checking problems for the A-hierarchy and the
W*-hierarchy. Thus we obtain very uniform characterisations of many
of the most important parameterized complexity classes in both formalisms.
Our results can be used to give new, simple proofs of some of the core results
of structural parameterized complexity theory.
|
Publication date: March 7, 2005
Full Text: PDF | PostScript
DOI: 10.2168/LMCS-1(1:2)2005
Hit Counts: 4280 |
 Creative Commons | |
