Geodesic
Complexity of linear and majority functions in the basis of antichain functions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 51-52

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The complexity circuits of Boolean functions is studied in a basis consisting of all characteristic functions of antichains over the Boolean cube. It is established that the circuit complexity of an $n$-variable parity function is $\left\lfloor \frac{n+1}{2}\right\rfloor$ and the complexity of its negation equals the complexity of the $n$-variable majority function which is $\left\lceil \frac{n+1}{2} \right\rceil$. 
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     author = {O. V. Podolskaya},
     title = {Complexity of linear and majority functions in the basis of antichain functions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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O. V. Podolskaya. Complexity of linear and majority functions in the basis of antichain functions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 51-52. http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a9/