Title: Circuit Lower Bounds Collapse Relativized Complexity Classes

in the 14th Annual Conference on Computational Complexity, pp. 222-226, 1999

Authors: Richard Beigel and Alexis Maciel

Abstract: Since the publication of Furst, Saxe, and Sipser's seminal paper connecting AC0 with the polynomial hierarchy, it has been well known that circuit lower bounds allow you to construct oracles that separate complexity classes. We will show that similar circuit lower bounds allow you to construct oracles that collapse complexity classes. For example, based on Hastad's parity lower bound, we construct an oracle such that P = PH ⊂ PARITYP = EXP.

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