C. Berg and S. Ulfberg. A lower bound for perceptrons and an oracle separation of the PP PH hierarchy. In Proceedings 12th Conference on Computational Complexity, pages 165--172. IEEE Computer Society Press, 1997.  Home/Search   Document Details and Download   Summary   Related Articles

....the 2nd Asian Computing Science Conference. by Hastad [Has88] He gave in detail oracle constructions by diagonalization, where the diagonalization essentially depends on circuit lower bounds. This approach has since then been employed fruitfully a number of times, see e.g. Has88, Ko89, Gre91, BU97] to name only very few examples. However, all the times the actual construction of the oracle requires a diagonalization where one has to show by a stage construction that a certain test language is not contained in a given complexity class. That the diagonalization works is always a ....

.... z k times ] and Theorem 4.4. q 5.4 The PP PH hierarchy Theorem 5.7. There is an oracle Y such that Sigma p;Y k 6 PP Sigma p;Y k 2 . Proof. Let f n k be the Sipser function [BS90] From Theorem 3. 1 we see that Sigma p k = BalancedLeaf P (f n k ) Berg and Ulfberg [BU97] show that f n k 62 qC[maj; z k 2 times ; log O(1) n) qC[maj; z k 2 times ; log O(1) n) Thus from Lemma 4.2 we see that f n k cannot be plt m reducible to depth k 1 perceptrons. The claim now follows from Theorem 4.4. q Konig s Lemma ....

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C. Berg and S. Ulfberg. A lower bound for perceptrons and an oracle separation of the PP PH hierarchy. In Proceedings 12th Conference on Computational Complexity, pages 165--172. IEEE Computer Society Press, 1997.

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