Geodesic
On complexity of realisation of linear Boolean functions by circuits of functional elements over the basis
Diskretnaya Matematika, Tome 15 (2003) no. 4, pp. 100-112.

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We show that the minimal circuit of functional elements over the basis $\{x\to y,\bar x\}$ which realises a linear function of $n$ variables consists of $4n-4$ elements. 
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I. C. Shkrebela. On complexity of realisation of linear Boolean functions by circuits of functional elements over the basis. Diskretnaya Matematika, Tome 15 (2003) no. 4, pp. 100-112. http://geodesic.mathdoc.fr/item/DM_2003_15_4_a5/

[1] Lupanov O. B., Asimptoticheskie otsenki slozhnosti upravlyaemykh sistem, MGU, Moskva, 1984

[2] Redkin N. P., “Dokazatelstvo minimalnosti nekotorykh skhem iz funktsionalnykh elementov”, Problemy kibernetiki, 1 23 (1970), 83–101 | MR

[3] Redkin N. P., “O minimalnoi realizatsii lineinoi funktsii skhemy iz funktsionalnykh elementov”, Kibernetika, 6 (1971), 31–38 | MR