Geodesic
Automata algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 4, pp. 37-66.

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

In this paper, we present the main results on problems of the expressibility and completeness for the automata theory, including the results for weakened problem statements. 
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V. B. Kudryavtsev. Automata algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 4, pp. 37-66. http://geodesic.mathdoc.fr/item/FPM_2009_15_4_a2/

[1] Dzh. Makkarti, K. Shennona (red.), Avtomaty, Izd. inostr. lit., M., 1956

[2] Alëshin S. V., “Konechnye avtomaty i problema Bernsaida o periodicheskikh gruppakh”, Mat. zametki, 11:3 (1972), 319–328 | MR | Zbl

[3] Alëshin S. V., “Ob otsutstvii bazisov v nekotorykh klassakh initsialnykh avtomatov”, Problemy kibernetiki, 22, 1970, 67–75

[4] Babin D. N., “Nerazreshimost problemy polnoty i $A$-polnoty nekotorykh sistem avtomatnykh funktsii”, Diskret. mat., 7:1 (1995), 52–65 | MR | Zbl

[5] Babin D. N., “Nerazreshimyi sluchai zadachi o polnote avtomatnykh funktsii”, Diskret. mat., 4:4 (1992), 41–55 | MR | Zbl

[6] Babin D. N., “O polnote dvukhmestnykh o. d. funktsii otnositelno superpozitsii”, Diskret. mat., 1:4 (1989), 86–91 | MR | Zbl

[7] Babin D. N., “O superpozitsiyakh ogranichenno-determinirovannykh funktsii”, Mat. zametki, 47:3 (1990), 3–10 | MR | Zbl

[8] Buevich V. A., “O $\tau$-polnote v klasse determinirovannykh funktsii”, DAN, 326:3 (1992), 399–403 | MR | Zbl

[9] Buevich V. A., “Ob algoritmicheskoi nerazreshimosti raspoznavaniya $A$-polnoty dlya ogranichenno-determinirovannykh funktsii”, Mat. zametki, 11:6 (1972), 687–697 | MR | Zbl

[10] Vetrennikova E. V., “Odin prostoi primer universalnoi o. d. funktsii”, Metody diskretnogo analiza v optimizatsii upravlyayuschikh sistem, Metody diskretnogo analiza, 40, In-t matematiki SO AN SSSR, Novosibirsk, 1983, 5–11

[11] Zakharova E. Yu., “Kriterii polnoty sistemy funktsii iz $P_k$”, Problemy kibernetiki, 18, 1967, 5–10 | Zbl

[12] Zakharova E. Yu., Kudryavtsev V. B., Yablonskii S. V., “O predpolnykh klassakh v $k$-znachnykh logikakh”, DAN SSSR, 186:3 (1969), 509–512 | Zbl

[13] Kon P., Universalnaya algebra, Mir, M., 1968 | MR

[14] Kratko M. I., “Algoritmicheskaya nerazreshimost problemy raspoznavaniya polnoty dlya konechnykh avtomatov”, DAN SSSR, 155:1 (1964), 35–37 | MR | Zbl

[15] Kudryavtsev V. B., “O moschnostyakh mnozhestv predpolnykh mnozhestv nekotorykh funktsionalnykh sistem, svyazannykh s avtomatami”, Problemy kibernetiki, 13, 1965, 45–74

[16] Kudryavtsev V. B., “Teorema polnoty dlya odnogo klassa avtomatov bez obratnykh svyazei”, Problemy kibernetiki, 8, 1962, 91–115

[17] Kudryavtsev V. B., Funktsionalnye sistemy, Izd-vo Mosk. un-ta, M., 1982 | Zbl

[18] Kudryavtsev V. B, Alëshin S. V., Podkolzin A. S., Vvedenie v teoriyu avtomatov, Nauka, M., 1985 | MR | Zbl

[19] Lo Chzhu-Kai, “Predpolnye klassy, opredelyaemye $k$-arnymi otnosheniyami v $k$-znachnoi logike”, Acta Sci. Natur. Univ. Jilin, 3 (1964)

[20] Lo Chzhu-Kai, Lyu Syui Khua, “Predpolnye klassy, opredelyaemye binarnymi otnosheniyami v mnogoznachnoi logike”, Acta Sci. Natur. Univ. Jilin, 4 (1963)

[21] Maltsev A. I., “Iterativnye algebry i mnogoobrazie Posta”, Algebra i logika, 5:2 (1966), 5–24 | MR | Zbl

[22] Martynyuk V. V., “Issledovanie nekotorykh klassov funktsii v mnogoznachnykh logikakh”, Problemy kibernetiki, 3, 1960, 49–60 | Zbl

[23] Pan Yun-Tsze, “Odin razreshayuschii metod dlya otyskaniya vsekh predpolnykh klassov v mnogoznachnoi logike”, Acta Sci. Natur. Univ. Jilin, 2 (1962)

[24] Chasovskikh A. A., “O polnote v klasse lineinykh avtomatov”, Matematicheskie voprosy kibernetiki, 3, 1995, 140–166 | MR

[25] Yablonskii S. V., “Funktsionalnye postroeniya v $k$-znachnoi logike”, Tr. MIRAN im. V. A. Steklova, 51, 1958, 5–142 | MR | Zbl

[26] Yablonskii S. V., Gavrilov G. P., Kudryavtsev V. B., Funktsii algebry logiki i klassy Posta, Nauka, M., 1966 | MR

[27] Yanov Yu. I., Muchnik A. A., “O suschestvovanii $k$-znachnykh zamknutykh klassov, ne imeyuschikh bazisa”, DAN SSSR, 127:1 (1959), 144–146

[28] Post E., Two-Valued Iterative Systems of Mathematical Logic, Princeton, 1941 | MR | Zbl

[29] Rosenberg I. G., “La structure des fonctions de plusiers variables sur un ensemble fini”, C. R. Acad. Sci. Paris, 260 (1965), 3817–3819 | MR | Zbl

[30] Rosenberg I., Hikata T., “Completeness for uniformly delayed circuits”, Proc. of the 13th Int. Symp. on Multiple-Valued Logic (Kyoto, Japan, May 23–25, 1983), 1–9

[31] Slupecki J., “Kriterium pelnosci wielowar tosciowych systemow logiki zdan”, C. R. Séances Soc. Sc. Lettr. Varsovie Cl. III, 32 (1939), 102–128