Geodesic
On minimal circuts in Sheffer basis for linear Boolean functions
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 4, pp. 65-87.

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

Realizations of pairity function and its negation by Boolean circuits in Sheffer basis are considered. The exact value of complexity of pairity function's negation is established. Another result is structure description of minimal circuits for the parity function. Ill. 13, bibliogr. 8.
Keywords: Boolean circuit, pairity function, Sheffer stroke. 
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Yu. A. Kombarov. On minimal circuts in Sheffer basis for linear Boolean functions. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 4, pp. 65-87. http://geodesic.mathdoc.fr/item/DA_2013_20_4_a5/

[1] Kombarov Yu. A., “O minimalnykh realizatsiyakh lineinykh bulevykh funktsii”, Diskret. analiz i issled. operatsii, 19:3 (2012), 39–57 | MR

[2] Lozhkin S. A., “O strukture minimalnykh skhem v bazise $\{\,\vee,\neg\}$, realizuyuschikh lineinuyu funktsiyu”, Tr. V Mezhdunar. konf. “Diskretnye modeli v teorii upravlyayuschikh sistem” (Ratmino, 26–29 maya 2003 g.), MGU, M., 2003, 50–51

[3] Lupanov O. B., Asimptoticheskie otsenki slozhnosti upravlyayuschikh sistem, MGU, M., 1984, 136 pp.

[4] Merekin Yu. V., “Nizhnyaya otsenka slozhnosti dlya skhem konkatenatsii slov”, Diskret. analiz i issled. operatsii, 3:1 (1996), 52–56 | MR | Zbl

[5] Redkin N. P., “Dokazatelstvo minimalnosti nekotorykh skhem iz funktsionalnykh elementov”, Probl. kibernetiki, 23, 1970, 83–101 | MR

[6] Redkin N. P., “O minimalnoi realizatsii lineinoi funktsii skhemoi iz funktsionalnykh elementov”, Kibernetika, 1971, no. 6, 31–38 | MR

[7] Redkin N. P., Diskretnaya matematika, Fizmatlit, M., 2009, 263 pp.

[8] Cardot C., “Quelques résultats sur l'application de l'algébre de Boole á la synthése des circuits á relais”, Ann. Telecomm., 7:2 (1952), 75–84 | MR