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Refined bounds on Shannon’s function for complexity of circuits of functional elements
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2022), pp. 32-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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Earlier, the author proposed rather general approaches and methods for obtaining high accuracy and close to high accuracy asymptotic bounds on Shannon's function for complexity in various classes of circuits. Most of the results obtained with their aid were published in a number of papers, except perhaps for the close to the high accuracy asymptotic bounds on Shannon's function for the complexity of circuits without restrictions on their structure. This paper fills this gap and presents a modified and simplified version of one of the above-mentioned methods, which, nevertheless, allows one to obtain bounds with the required accuracy. 
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S. A. Lozhkin. Refined bounds on Shannon’s function for complexity of circuits of functional elements. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2022), pp. 32-40. http://geodesic.mathdoc.fr/item/VMUMM_2022_3_a6/

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

[2] Lupanov O.B., Asimptoticheskie otsenki slozhnosti upravlyayuschikh skhem, Izd-vo Mosk. un-ta, M., 1984

[3] Lozhkin S.A., Lektsii po osnovam kibernetiki, Izdatelskii otdel fakulteta VMiK MGU im. M. V. Lomonosova, M., 2004

[4] Lupanov O.B., “Ob odnom metode sinteza skhem”, Izv. vuzov. Radiofizika, 1 (1958), 120–140

[5] Lupanov O.B., “O slozhnosti realizatsii funktsii algebry logiki formulami”, Problemy kibernetiki, 3, Fizmatgiz, M., 1960, 61–80

[6] Lozhkin S.A., “Otsenki vysokoi stepeni tochnosti dlya slozhnosti upravlyayuschikh sistem iz nekotorykh klassov”, Matematicheskie voprosy kibernetiki, 6, Nauka, M., 1996, 189–214 | MR

[7] Lozhkin S.A., Asimptoticheskie otsenki vysokoi stepeni tochnosti dlya slozhnosti upravlyayuschikh sistem, Dokt. dis., M., 1997

[8] Lozhkin S.A., “O sinteze formul, slozhnost i glubina kotorykh ne prevoskhodyat asimptoticheski nailuchshikh otsenok vysokoi stepeni tochnosti”, Vestn. Mosk. un-ta. Matem. Mekhan., 2007, no. 3, 19–25 | Zbl

[9] Lozhkin S.A., Shiganov A.E., “High accuracy asymptotic bounds on the BDD size and weight of the hardest functions”, Fundamenta Informaticae, 104:3 (2010), 239–253 | DOI | MR | Zbl

[10] Lozhkin S.A., Konovodov V.A., “O sinteze i slozhnosti formul s ogranichennoi glubinoi alternirovaniya”, Vestn. Mosk. un-ta. Vychisl. matem. i kibern., 2012, no. 2, 28–36 | Zbl