A Uniform Circuit Lower Bound for the Permanent

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the new circuit consists of a subexponential number of circuits, each of which is of subex-ponential size, the new circuit is also of subexponential size. The depth of the new circuit family is the same as fC n g but the top layer of MOD p gates has been \absorbed" into the symmetric gate computing B and been replaced by a layer of AND gates of small fan-in. Now, by an appeal to Lemma 9, the circuit can be converted into nice form, which completes the proof. (of Theorem 3) By Lemma 16, every language in ACC(subexp) is accepted by a deterministic SYMACC circuit family of subexponential size, with small fan-in AND gates, no OR gates, and no MOD m gates for composite m. Successive applications of Lemma 17 and Lemma 18 remove all MOD gates from the circuit, while maintaining the property that all AND gates have small fan-in. This suces to prove the theorem.

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تاریخ انتشار 1993