40 research outputs found
Self-Specifying Machines
We study the computational power of machines that specify their own
acceptance types, and show that they accept exactly the languages that
\manyonesharp-reduce to NP sets. A natural variant accepts exactly the
languages that \manyonesharp-reduce to P sets. We show that these two classes
coincide if and only if \psone = \psnnoplusbigohone, where the latter class
denotes the sets acceptable via at most one question to \sharpp followed by
at most a constant number of questions to \np.Comment: 15 pages, to appear in IJFC
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On the Power of Probabilistic Polynomial Time: PNP[log] ⊆ PP
We show that every set in the ΘP2 level of the polynomial hierarchy -- that is, every set polynomial-time truth-table reducible to SAT -- is accepted by a probabilistic polynomialtime Turing machine: PNP[log] ⊆ PP
Reducing the Number of Solutions of NP Functions
AbstractWe study whether one can prune solutions from NP functions. Though it is known that, unless surprising complexity class collapses occur, one cannot reduce the number of accepting paths of NP machines, we nonetheless show that it often is possible to reduce the number of solutions of NP functions. For finite cardinality types, we give a sufficient condition for such solution reduction. We also give absolute and conditional necessary conditions for solution reduction, and in particular we show that in many cases solution reduction is impossible unless the polynomial hierarchy collapses