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New Collapse Consequences of NP Having Small Circuits
1998
SIAM journal on computing (Print)
We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomial-time hierarchy PH to ZPP(NP) under the assumption that NP has polynomial-size circuits. This improves on the well-known result of Karp, Lipton, and Sipser [KL80] stating a collapse of PH to its second level Σ P 2 under the same assumption. As a further consequence, we derive new collapse consequences under the
doi:10.1137/s0097539795296206
fatcat:fgjq46fytfh2rfxp6tphe463wm