Geodesic
Complexity of realization of a linear Boolean function in Sheffer's basis
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 49-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is focused on realization of linear Boolean functions by circuits of functional elements in the basis $\left\{\overline{x \& y}\right\}$. The exact value of complexity of negation of linear function is obtained in this paper. Another result is the description of all minimal circuts realizing a linear function. 
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     title = {Complexity of realization of a linear {Boolean} function in {Sheffer's} basis},
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Yu. A. Kombarov. Complexity of realization of a linear Boolean function in Sheffer's basis. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 49-53. http://geodesic.mathdoc.fr/item/VMUMM_2013_2_a10/

[1] Yablonskii S.V., Vvedenie v diskretnuyu matematiku, Nauka, M., 1986 | MR

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

[3] Lupanov O. B., Asimptoticheskie otsenki slozhnosti upravlyayuschikh sistem, Izd-vo MGU, M., 1984

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

[5] Kombarov Yu.A., “O minimalnykh realizatsiyakh lineinykh bulevykh funktsii skhemami iz funktsionalnykh elementov v bazise $\{x\rightarrow y, \overline{x} \ y\}$”, Tr. VIII Mezhdunar. konf. “Diskretnye modeli v teorii upravlyayuschikh sistem” (Moskva, 6–9 aprelya 2009 g.), MAKS Press, M., 2009, 145–149

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

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

[8] Kombarov Yu.A., “O minimalnykh skhemakh dlya lineinykh bulevykh funktsii”, Vestn. Mosk. un-ta. Matem. Mekhan., 2011, no. 6, 41–44 | MR

[9] Redkin N.P., “O minimalnykh i asimptoticheski minimalnykh skhemakh dlya nekotorykh individualnykh bulevykh funktsii”, Mat-ly IX Mezhdunar. seminara “Diskretnaya matematika i ee prilozheniya”, posvyaschennogo 75-letiyu so dnya rozhdeniya akademika O.B. Lupanova (Moskva, 18–23 iyunya 2007 g.), Izd-vo TsPI pri mekh.-mat. f-te MGU, M., 2007, 11–19

[10] Redkin N.P., “O minimalnoi realizatsii dvoichnogo summatora”, Problemy kibernetiki, 38, Nauka, M., 1981, 181–216

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