46 research outputs found
Genericity and measure for exponential time
AbstractRecently, Lutz [14, 15] introduced a polynomial time bounded version of Lebesgue measure. He and others (see e.g. [11, 13–18, 20]) used this concept to investigate the quantitative structure of Exponential Time (E = DTIME(2lin)). Previously, Ambos-Spies et al. [2, 3] 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 nc-generic sets has p-measure 1. This allows us to simplify and extend certain p-measure 1-results. To illustrate the power of generic sets we take the Small Span Theorem of Juedes and Lutz [11] as an example and prove a generalization for bounded query reductions
The mathematical foundations of randomness
Contains fulltext :
158162.pdf (publisher's version ) (Open Access
The finite intervals of the Muchnik lattice
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91467.pdf (publisher's version ) (Open Access)
Contains fulltext :
91467.pdf (preprint version ) (Open Access
Generalizations of the Weak Law of the Excluded Middle
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91850.pdf (publisher's version ) (Open Access
Intuitionistic Logic and Computability Theory
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83387.pdf (publisher's version ) (Closed access