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dc.contributor.authorCai, Jin-yien_US
dc.description.abstractThis thesis is a study of separations of some complexity classes which take place in almost all relativized worlds. We achieve probability one separations of PSPACE from the Polynomial-time Hierarchy PH. Also we separate with probability one all levels of the Boolean Hierarchy BH. The study on the Boolean Hierarchy is a continuation of the work by Bennet and Gill in [BG81] and the joint work in [CH86], where we introduced the "sawing" argument. This "sawing" technique is adapted here to yield probability one separation. The study on PSPACE versus the Polynomial-time Hierarchy is more intriguing. Several novel techniques are employed here. The connection with Boolean circuit is exploited to reduce the problem to a Boolean circuit computation problem. The fixed depth unbounded fan-in Boolean circuit model is considered in connection with the parity function. We show that with an exponential bound of the form $exp(n^{\lambda}$ on the size of the circuits, they make asymptomatically 50% error on all possible inputs, uniformly. Certain probabilistic and game theoretic methods are applied extensively to conclude the result.en_US
dc.format.extent3332730 bytes
dc.format.extent716712 bytes
dc.publisherCornell Universityen_US
dc.subjectcomputer scienceen_US
dc.subjecttechnical reporten_US
dc.titleOn Some Most Probable Separations of Complexity Classesen_US
dc.typetechnical reporten_US

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