Automata in algebra
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 23-32.

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In this article, some algebraical problems are considered. Several aspects of automaton theory and algebraical structures needed to obtain solutions of the problems are discussed.
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S. V. Aleshin. Automata in algebra. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 23-32. http://geodesic.mathdoc.fr/item/FPM_2009_15_3_a3/

[1] M. A. Arbiba (red.), Algebraicheskaya teoriya avtomatov, yazykov i polugrupp, Statistika, M., 1975 | MR

[2] Alëshin S. V., “O bazisakh v gruppakh avtomatnykh podstanovok”, Diskretnyi analiz, 17, 1970, 111–136

[3] Alëshin S. V., “Ob otsutstvii bazisov v nekotorykh klassakh initsialnykh avtomatov”, Problemy kibernetiki, 22, 1970, 33–58

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

[5] Alëshin S. V., “Ob odnom sledstvii teoremy Krona–Roudza”, Diskret. mat., 11:4 (1999), 101–109 | DOI | MR | Zbl

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

[7] Glushkov V. M., “Abstraktnaya teoriya avtomatov”, Uspekhi mat. nauk, 16:5 (1961), 3–62 | MR | Zbl

[8] Grigorchuk R. I., “K probleme Milnora o gruppovom roste”, DAN SSSR, 271:1 (1983), 101–109 | MR

[9] Zarovnyi V. P., “Avtomatnye podstanovki i spleteniya grupp”, DAN SSSR, 160:3 (1965), 128–144 | MR

[10] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, M., 1972 | MR | Zbl

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

[12] Makarov V. V., “O gruppakh avtomatnykh perestanovok”, Fundament. i prikl. mat., 2:1 (1996), 171–186 | MR | Zbl

[13] Malygin V. I., “Transformatsii gruppy avtomata pod deistviem operatsii obratnoi svyazi”, VI Vsesoyuzn. konf. po teoret. probl. kibernetiki, 1983

[14] Malygin V. I., Algebraicheskie invarianty kompozitsii avtomatov, Dis. $\dots$ kand. fiz.-mat. nauk, 1988

[15] Rozhkov A. V., “K teorii grupp alëshinskogo tipa”, Mat. zametki, 40:5 (1986), 572–589 | MR | Zbl

[16] Chasovskikh A. A., “Ob algoritmicheskoi razreshimosti problemy polnoty dlya lineinykh avtomatov”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1985, no. 2, 47–61

[17] Żuk A., “Groupes engendrés par les automates”, Astérisque, 317 (2008), 141–174 | MR | Zbl