Geodesic
Lower bound of circuit complexity of parity function in a basis of unbounded fan-in
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2021), pp. 48-51

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The paper is focused on realization of parity functions by circuits in the basis $U_\infty$. This basis contains all functions of the form $x_1^{\sigma_1}\\ldots\ x_k^{\sigma_k}$. It is proved that every circuit over $U_\infty$ computing a parity function of $n$ variables contains at least $2\frac{1}{9}n+\Theta(1)$ gates. 
@article{VMUMM_2021_6_a7,
     author = {Yu. A. Kombarov},
     title = {Lower bound of circuit complexity of parity function in a basis of unbounded fan-in},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {48--51},
     publisher = {mathdoc},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_6_a7/}
}
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Yu. A. Kombarov. Lower bound of circuit complexity of parity function in a basis of unbounded fan-in. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2021), pp. 48-51. http://geodesic.mathdoc.fr/item/VMUMM_2021_6_a7/