Valiant’s Polynomial-Size Monotone Formula for Majority
نویسنده
چکیده
The existence of polynomial-size (monotone) formulae is known to be equivalent to the existence of logarithmic-depth (monotone) circuits of bounded fan-in. Anyhow, we shall prove the existence of logarithmic-depth monotone formulae (of bounded fan-in) for majority. Actually, two radically different proofs are known: The first proof uses a rather complicated construction of sorting networks of logarithmic depth [1, 2]. The second proof, presented below, uses the probabilistic method.
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تاریخ انتشار 2011