Reviewing Bounds on the Circuit Size of the Hardest Functions
DOI:
https://doi.org/10.7146/brics.v12i9.21875Resumé
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 be2^n / 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 lower bound valid for the full binary basis, and we give an explicit proof of the upper bound valid for the basis {not, and, or}.
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2005-03-11
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Frandsen, G. S., & Miltersen, P. B. (2005). Reviewing Bounds on the Circuit Size of the Hardest Functions. BRICS Report Series, 12(9). https://doi.org/10.7146/brics.v12i9.21875
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