论文信息 - Lower Bounds for Constant-Depth Circuits in the Presence of Help Bits

Lower Bounds for Constant-Depth Circuits in the Presence of Help Bits

Abstract We consider the problem of how many extra bits of “help” a constant-depth Boolean circuit needs in order to compute m functions of the same input. Each help bit can be an arbitrary Boolean function of the input. We prove an exponential lower bound on the size of the circuit computing m parity functions in the presence of m - 1 help bits. The proof is carried out using the algebraic machinery of Razborov and Smolensky. A by-product of the proof is that the same bound holds for circuits with Modp gates for a fixed prime p > 2. The lower bound implies a random oracle separation for PH and PSPACE, which is optimal in a technical sense.

Jin-Yi Cai

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