Geodesic
Complexity of implementation of parity functions in the implication--negation basis
Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 73-97.

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

The paper is concerned with circuits in the basis $\{x \to y, \overline{x}\}$. The exact value of the complexity of implementation of an even parity function is obtained and the minimal circuits implementing an odd parity function are described.
Keywords: circuit, parity function, minimal circuit, complexity circuits. 
@article{DM_2015_27_1_a5,
     author = {Yu. A. Kombarov},
     title = {Complexity of implementation of parity functions in the implication--negation basis},
     journal = {Diskretnaya Matematika},
     pages = {73--97},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_1_a5/}
}
TY  - JOUR
AU  - Yu. A. Kombarov
TI  - Complexity of implementation of parity functions in the implication--negation basis
JO  - Diskretnaya Matematika
PY  - 2015
SP  - 73
EP  - 97
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2015_27_1_a5/
LA  - ru
ID  - DM_2015_27_1_a5
ER  - 
%0 Journal Article
%A Yu. A. Kombarov
%T Complexity of implementation of parity functions in the implication--negation basis
%J Diskretnaya Matematika
%D 2015
%P 73-97
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2015_27_1_a5/
%G ru
%F DM_2015_27_1_a5
Yu. A. Kombarov. Complexity of implementation of parity functions in the implication--negation basis. Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 73-97. http://geodesic.mathdoc.fr/item/DM_2015_27_1_a5/

[1] Lupanov O. B., Asimptoticheskie otsenki slozhnosti upravlyayuschikh sistem, MGU, M., 1984

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

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

[4] Redkin N.P., Diskretnaya matematika, Fizmatlit, M., 2009

[5] Ugolnikov A.B., Klassy Posta, Iz-vo Tsentra prikl. issled. pri mekh.-mat. f-te MGU, M., 2008

[6] Shkrebela I.S., “O slozhnosti realizatsii lineinykh bulevykh funktsii skhemami iz funktsionalnykh elementov v bazise $\{x \to y, \overline{x}\} $”, Diskretnaya matematika, 15:4 (2003), 100–112 | DOI | Zbl