Geodesic
Inversion complexity of self-correcting circuits for a certain sequence of Boolean functions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 58-61

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It is stated that the inversion complexity $L_k^{-}(f^n_2)$ of monotone symmetric Boolean functions $f_2^n(x_1,\ldots,x_n)=\bigvee \limits_{1\leq i$ by $k$-self-correcting schemes in the basis $B=\{\,-\}$ for growing $n$ asymptotically equals $n\min\{k+1,p\}$ when the price of a reliable inventor $p\geq1$ and $k$ are fixed. 
@article{VMUMM_2012_3_a12,
     author = {T. I. Krasnova},
     title = {Inversion complexity of self-correcting circuits for a certain sequence of {Boolean} functions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {58--61},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a12/}
}
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T. I. Krasnova. Inversion complexity of self-correcting circuits for a certain sequence of Boolean functions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 58-61. http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a12/