LWPP and WPP are not uniformly gap-definable

Authors:
Holger Spakowski;Rahul Tripathi
Affiliations:
Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany;Department of Computer Science and Engineering, University of South Florida, Tampa, FL 33620, USA
Venue:
Journal of Computer and System Sciences
Year:
2006

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Abstract

Resolving an issue open since Fenner, Fortnow, and Kurtz raised it in [S. Fenner, L. Fortnow, S. Kurtz, Gap-definable counting classes, J. Comput. System Sci. 48 (1) (1994) 116-148], we prove that LWPP is not uniformly gap-definable and that WPP is not uniformly gap-definable. We do so in the context of a broader investigation, via the polynomial degree bound technique, of the lowness, Turing hardness, and inclusion relationships of counting and other central complexity classes.