Abstract

We give improved lower bounds for the size of small depth circuits computing several functions. In particular we prove almost optimal lower bounds for the size of parity circuits. Fur-ther we show that there are functions computable in polynomial size and depth k but requires ex-ponential size when the depth is restricted to k-1. Our main lemma which is of independent interest states that by using a random restriction we can convert an AND of small ORs to an OR of small ANDs and conversely.

Citations

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