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 
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/
@article{DM_2003_15_4_a5,
     author = {I. C. Shkrebela},
     title = {On complexity of realisation of linear {Boolean} functions by circuits of functional elements over the basis},
     journal = {Diskretnaya Matematika},
     pages = {100--112},
     year = {2003},
     volume = {15},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2003_15_4_a5/}
}
TY  - JOUR
AU  - I. C. Shkrebela
TI  - On complexity of realisation of linear Boolean functions by circuits of functional elements over the basis
JO  - Diskretnaya Matematika
PY  - 2003
SP  - 100
EP  - 112
VL  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/DM_2003_15_4_a5/
LA  - ru
ID  - DM_2003_15_4_a5
ER  - 
%0 Journal Article
%A I. C. Shkrebela
%T On complexity of realisation of linear Boolean functions by circuits of functional elements over the basis
%J Diskretnaya Matematika
%D 2003
%P 100-112
%V 15
%N 4
%U http://geodesic.mathdoc.fr/item/DM_2003_15_4_a5/
%G ru
%F DM_2003_15_4_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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