Andrew Yao. Separating the polynomial-time hierarchy by oracles. In Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, pages 1--10, Los Angeles, Ca., USA, October 1985. IEEE Computer Society Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Tardos [45] managed to give a similar lower bound for a function that was computable in P, which dashed any hopes of trying to separate P from NP using monotone circuit techniques. The other line of attack was on lower bounds for constant depth circuits. The initial results of Yao [50], and Furst, Saxe and Sipser [20] were improved by H astad [26] to give optimal, exponential lower bounds for computing the parity function using constant depth circuits. In contrast to circuits of constant depth, there are no known lower bounds for circuits that have unbounded depth. This should ....

Andrew Yao. Separating the polynomial-time hierarchy by oracles. In Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science, pages 1--10, Los Angeles, Ca., USA, October 1985. IEEE Computer Society Press.

....about the polynomial time hierarchy. This fact was first established by Furst, Saxe, and Sipser [5] Sipser [13] later defined a family of functions that are computable by linear size circuits of depth k, and showed that they require super polynomial size boolean circuits of depth k Gamma 1. Yao [14] and Hstad [8, 9] improved Sipser s result by showing that the same functions actually require exponential size circuits of depth k Gamma 1; this fact implies the existence of an oracle that separates the levels in the polynomial time hierarchy. There is a similar correspondence between the ....

Andrew Yao. Separating the polynomial-time hierarchy by oracles. In Proceedings of the 26th IEEE Symposium on Foundations of Computer Science, pages 1--10, 1985. 17

.... Bounds for (MOD p MOD m) Circuits Preliminary version Vince Grolmusz G abor Tardos y Abstract Modular gates are known to be immune for the random restriction techniques of Ajtai [Ajt83] Furst, Saxe, Sipser [FSS84] Yao [Yao85] and Hastad [Has86] We demonstrate here a random clustering technique which overcomes this difficulty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Th erien [BST90] Krause and Pudl ak [KP94] and others, characterizing ....

....models of computation. They are used in VLSI design, and in complexity theory as well as in the theory of parallel computation. A majority of the strongest and deepest lower bound results for computational complexity were proved using the Boolean circuit model of computation (for example [Raz85] [Yao85], Has86] Raz87] Smo87] or see [vL90] for a survey) Unfortunately, lots of questions even for very restricted circuit classes have been unsolved for a long time. Bounded depth and polynomial size is a natural restriction. Ajtai [Ajt83] Furst, Saxe, and Sipser [FSS84] proved that ....

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Andrew C. Yao. Separating the polynomial-time hierarchy by oracles. In Proc. 26th Ann. IEEE Symp. Found. Comput. Sci., pages 1--10, 1985.

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Andrew Chi-Chih Yao,"Separating the Polynomial-Time Hierarchy by Oracles, " 26th IEEE Symp. on Foundations of Comp. Sci., 1985, 1-10.

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