Some observations on NP real numbers and P-selective sets |
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Authors: | Alan L. Selman |
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Affiliation: | Department of Computer Science, Iowa State University, Ames, Iowa, USA 50011 |
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Abstract: | We show that each standard left cut of a real number is a p-selective set. Classification results about NP real numbers and recursively enumerable real numbers follow from similar results about p-selective and semirecursive sets. In particular, it is proved that no left cut can be NP-hard unless the polynomial hierarchy collapses to ?2P. This result is surprising because it shows that the McLaughlin-Martin construction of a ?tt-complete r.e. semirecursive set fails at the polynomial time complexity level. |
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