Complexity of realization of Boolean functions from some classes related to finite grammars by formulas of alternation depth $3$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2014), pp. 14-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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The realization complexity of Boolean functions associated with finite grammars in the class of formulae of alternation depth 3 is studied. High accuracy asymptotic bounds are obtained for the corresponding Shannon function.
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S. A. Lozhkin; V. A. Konovodov. Complexity of realization of Boolean functions from some classes related to finite grammars by formulas of alternation depth $3$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2014), pp. 14-19. http://geodesic.mathdoc.fr/item/VMUMM_2014_3_a2/

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

[2] Lozhkin S.A., “Otsenki vysokoi stepeni tochnosti dlya slozhnosti upravlyayuschikh sistem iz nekotorykh klassov”, Matematicheskie voprosy kibernetiki, 6, Fizmatlit, M., 1996, 189–213 | MR

[3] Lupanov O.B., “O realizatsii funktsii algebry logiki formulami iz konechnykh klassov (formulami ogranichennoi glubiny) v bazise $\,\vee,\overline{\phantom{a}}$”, Problemy kibernetiki, 6, Fizmatgiz, M., 1961, 5–14

[4] 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 | MR | Zbl

[5] Lozhkin S.A., “Asimptoticheskie otsenki vysokoi stepeni tochnosti dlya slozhnosti funktsii, svyazannykh s avtomatnymi yazykami”, Problemy teoreticheskoi kibernetiki, Tez. dokl. XII Mezhdunar. konf., v. II, ed. O. B. Lupanov, Izd-vo TsPI pri mekh.-mat. f-te MGU, M., 1999, 138

[6] Kondratov A.V., “Asimptoticheskie otsenki vysokoi stepeni tochnosti dlya slozhnosti realizatsii funktsii, svyazannykh s avtomatnymi yazykami, v nekotorykh klassakh skhem”, Matematicheskie voprosy kibernetiki, 13, Fizmatlit, M., 2004, 279–288 | MR

[7] Lozhkin S.A., Lektsii po osnovam kibernetiki, Ucheb. posobie, Izd. otdel f-ta VMiK MGU, M., 2004

[8] Chomsky N., Miller G.A., “Finite state languages”, Inf. and Control, 1 (1958), 91–112 ; Khomskii N., Miller Dzh.A., “Yazyki s konechnym chislom sostoyanii”, Kibernet. sb., 4 (1962), 233–255 | DOI | MR