Abstract
We consider depth-2 and 3 circuits over the basis consisting of all Boolean functions. For depth-3 circuits, we prove a lower bound Ω(nlogn) for the size of any circuit computing the cyclic convolution. For depth-2 circuits, a lower bound Ω(n 3/2) for the same function was obtained in our previous paper [10]. Here we present an improved proof of this bound. Both lower bounds are the best known for depth-3 and depth-2 circuits, respectively.
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Cherukhin, D.Y. (2008). Lower Bounds for Depth-2 and Depth-3 Boolean Circuits with Arbitrary Gates. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds) Computer Science – Theory and Applications. CSR 2008. Lecture Notes in Computer Science, vol 5010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79709-8_15
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DOI: https://doi.org/10.1007/978-3-540-79709-8_15
Publisher Name: Springer, Berlin, Heidelberg
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