Reviewing bounds on the circuit size of the hardest functions


In this paper we review the known bounds for L(n), the circuit size complexity of the hardest Boolean function on n input bits. The best known bounds appear to be 2 n (1 + log n n −O( 1 n )) ≤ L(n) ≤ 2 n n (1 + 3 log n n + O( 1 n )) However, the bounds do not seem to be explicitly stated in the literature. We give a simple direct elementary proof of the… (More)
DOI: 10.1016/j.ipl.2005.03.009


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