Ming-Jye Sheu

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Based on the ε- and Δ-classes of the polynomial-time hierarchy, Schöning [S1], [S3]introduced low and high hierarchies within NP Several classes of sets have been located in the bottom few levels of these hierarchies [S1], [S3], [KS], [BB], [BS2], [AH]. Most results placing sets in the Δ-levels of the low hierarchy are related to sparse sets, and the proof(More)
The low and high hierarchies within NP were introduced by Schöning in order to classify sets in NP. It is not known whether the low and high hierarchies include all sets in NP. In this paper, using the circuit lower-bound techniques of Håstad and Ko, we construct an oracle set relative to which UP contains a language that is not in any level of the low(More)
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