J. Tarui, "Randomized Polynomials, Threshold Circuits, and the Polynomial Hierarchy ", Proceedings of the 8th Annual Symposium on Theoretical Aspects of Computer Science (1991) 238-250.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[18] that PP PH P PP combined with a theorem of Tor an [22] which states NP PP = NP C=P . It is significant since it states that C=P is hard for the polynomial hierarchy under nondeterministic reductions. Fact (ii) was proved by Toda and Ogiwara [20] and in a stronger form by Tarui [16]. It is significant since it says that C=P is hard for the polynomial hierarchy under randomized reductions. The purpose of this paper is to observe that although C=P is quite powerful under nondeterministic or randomized reductions, nevertheless under deterministic reductions it appears to be ....

J. Tarui, "Randomized Polynomials, Threshold Circuits, and the Polynomial Hierarchy ", Proceedings of the 8th Annual Symposium on Theoretical Aspects of Computer Science (1991) 238-250.

....Some interesting results for perceptrons were also obtained by Beigel, Reingold and Spielman [3] as a consequence of the closure under intersection of PP. Further related results and extensions have been obtained by Beigel, Reingold and Spielman [4] Aspnes, Beigel, Furst and Rudich [2] and Tarui [11]. An interesting open question left by the work of [6] is whether there is an oracle separating the hierarchy PP PH . More precisely, is there an oracle A such that the following is true: 8d) PP Sigma p;A d 1 6 PP Sigma p;A d ) Indeed, in light of surprising results such as Toda s ....

J. Tarui, "Randomized Polynomials, Threshold Circuits, and the Polynomial Hierarchy", in 8th Annual Symposium on Theoretical Aspects of Computer Science, Springer-Verlag LNCS 480, (1991) 238-250.

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