dc.contributor.author Cai, Jin-yi en_US dc.date.accessioned 2007-04-23T17:16:02Z dc.date.available 2007-04-23T17:16:02Z dc.date.issued 1986-08 en_US dc.identifier.citation http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR86-778 en_US dc.identifier.uri https://hdl.handle.net/1813/6618 dc.description.abstract This 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.extent 3332730 bytes dc.format.extent 716712 bytes dc.format.mimetype application/pdf dc.format.mimetype application/postscript dc.language.iso en_US en_US dc.publisher Cornell University en_US dc.subject computer science en_US dc.subject technical report en_US dc.title On Some Most Probable Separations of Complexity Classes en_US dc.type technical report en_US
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