CT-1994-10: Genericity and Measure for Exponential Time

CT-1994-10: Ambos-Spies, Klaus and Neis, Hans-Christian and Terwijn, Sebastiaan A. (1994) Genericity and Measure for Exponential Time. [Report]

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Abstract

Recently Lutz introduced a polynomial time bounded version of Lebesgue
measure. He and others used this concept to investigate the quantitative
structure of Exponential Time (E=DTIME(2^lin)). Previously, Ambos­Spies,
Fleischhack and Huwig introduced polynomial time bounded genericity
concepts and used them for the investigation of structural properties of
NP (under appropriate assumptions) and E. Here we relate these concepts
to each other. We show that, for any c>=1, the class of n^c­generic sets
has p­measure 1. This allows us to simplify and extend certain
p­measure 1­results. To illustrate the power of generic sets we take the
Small Span Theorem of Juedes and Lutz as an example and prove a
generalization for bounded query reductions.

Item Type:	Report
Report Nr:	CT-1994-10
Series Name:	Computation and Complexity Theory (CT)
Year:	1994
Date Deposited:	12 Oct 2016 14:39
Last Modified:	12 Oct 2016 14:39
URI:	https://eprints.illc.uva.nl/id/eprint/1058

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