F. Green, "An oracle separating \PhiP from PP PH ", Information Processing Letters 37 (1991) 149-153.  Home/Search   Document Not in Database   Summary   Related Articles

....the monotone version of a problem which, in the general case, would imply an oracle separation of PP PH . 1 Introduction Recently perceptrons (see definition below) have received some renewed attention because of their relevance to some important issues in structural complexity theory. In [6] it was shown that perceptrons cannot compute parity unless they are of exponential size 1 . This has the consequence that (9A) PhiP 6 PP PH A ) A result for perceptrons of depth 2 was used by Beigel [5] to provide an oracle A such that P NP A 6 PP A . Some interesting results for ....

....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 theorem [12] one might wonder if it is possible that PP ....

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F. Green, "An oracle separating \PhiP from PP PH ", Information Processing Letters 37 (1991) 149-153.

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