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June 2007 An analysis of the W*-hierarchy
Yijia Chen, Jörg Flum, Martin Grohe
J. Symbolic Logic 72(2): 513-534 (June 2007). DOI: 10.2178/jsl/1185803622

Abstract

We observe that the W*-hierarchy, a variant (introduced by Downey, Fellows, and Taylor [7]) of the better known W-hierarchy, coincides with the W-hierarchy, though not level wise, but just as a whole hierarchy. More precisely, we prove that W[t]⊆W*[t]⊆ W[2t-2] for each t≥ 2. It was known before that W[1]=W*[1] and W[2]=W*[2]. Our second main result is a new logical characterization of the W*-hierarchy in terms of “Fagin-definable problems.” As a by-product, we also obtain an improvement of our earlier characterization of the hierarchy in terms of model-checking problems. Furthermore, we obtain new complete problems for the classes W[3] and W*[3].

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Yijia Chen. Jörg Flum. Martin Grohe. "An analysis of the W*-hierarchy." J. Symbolic Logic 72 (2) 513 - 534, June 2007. https://doi.org/10.2178/jsl/1185803622

Information

Published: June 2007
First available in Project Euclid: 30 July 2007

zbMATH: 1122.03040
MathSciNet: MR2320289
Digital Object Identifier: 10.2178/jsl/1185803622

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 2 • June 2007
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