Geodesic
Criteria of decomposability of the Post's clones
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 3, pp. 2-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Problem of realization of Boolean functions using the formulas of special kind is considered in this paper. Notion of completion of the systems of Boolean functions is introduced. Criteria of decomposability of the completions to the intersection of simpler completions is obtained.
Keywords: paper
Mots-clés : contains. 
@article{IIGUM_2013_6_3_a0,
     author = {Y. V. Akulov},
     title = {Criteria of decomposability of the {Post's} clones},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {2--24},
     year = {2013},
     volume = {6},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a0/}
}
TY  - JOUR
AU  - Y. V. Akulov
TI  - Criteria of decomposability of the Post's clones
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2013
SP  - 2
EP  - 24
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a0/
LA  - ru
ID  - IIGUM_2013_6_3_a0
ER  - 
%0 Journal Article
%A Y. V. Akulov
%T Criteria of decomposability of the Post's clones
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2013
%P 2-24
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a0/
%G ru
%F IIGUM_2013_6_3_a0
Y. V. Akulov. Criteria of decomposability of the Post's clones. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 3, pp. 2-24. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_3_a0/

[1] Ya. V. Akulov, “O polnote sistem funktsii dlya klassov rasshirennoi superpozitsii”, Vestn. MGU. Matematika. Mekhanika, 2011, no. 1, 36–41

[2] Yu. V. Golunkov, “Polnota sistem funktsii v operatornykh algoritmakh, realizuyuschikh funktsii $k$-znachnoi logiki”, Veroyatnost. metody i kibernetika, 1980, no. 17, 23–34 | MR

[3] O. M. Kasim-Zade, “O metricheskikh svoistvakh obobschennykh invariantnykh klassov”, Matematicheskie voprosy kibernetiki, 15, Nauka, M., 2006, 9–34

[4] Yu. V. Kuznetsov, “O klassakh bulevykh funktsii, invariantnykh otnositelno otozhdestvleniya peremennykh”, Dokl. AN SSSR, 290:4 (1986), 780–785 | MR

[5] A. V. Kuznetsov, “O sredstvakh dlya obnaruzheniya nevyvodimosti i nevyrazimosti”, Logicheskii vyvod, Nauka, M., 1979, 5–33

[6] S. S. Marchenkov, “Osnovnye otnosheniya $S$-klassifikatsii funktsii mnogoznachnoi logiki”, Diskret. matematika, 8:1 (1996), 99–128 | DOI | MR

[7] S. S. Marchenkov, A. B. Ugolnikov, Zamknutye klassy bulevykh funktsii, Izd-vo IPM AN SSSR, M., 1990 | MR

[8] S. S. Marchenkov, Zamknutye klassy bulevykh funktsii, Fizmatlit, M., 2000 | MR

[9] Nguen Van Khoa, “O semeistvakh zamknutykh klassov $k$-znachnoi logiki, sokhranyaemykh vsemi avtomorfizmami”, Diskret. matematika, 5:4 (1993), 87–108 | MR

[10] V. D. Solovev, “Zamknutye klassy v $k$-znachnoi logike s operatsiei razvetvleniya po predikatam”, Diskret. matematika, 2:4 (1990), 18–25 | MR

[11] V. A. Taimanov, “O funktsionalnykh sistemakh $k$-znachnoi logiki s operatsiyami programmnogo tipa”, Dokl. AN SSSR, 268:6 (1983), 1307–1310 | MR

[12] O. S. Tarasova, “Klassy $k$-znachnoi logiki, zamknutye otnositelno rasshirennoi operatsii superpozitsii”, Vestn. MGU. Matematika. Mekhanika, 2001, no. 6, 54–57 | MR

[13] O. S. Tarasova, “Klassy funktsii trekhznachnoi logiki, zamknutye otnositelno operatsii superpozitsii i perestanovok”, Matematicheskie voprosy kibernetiki, 13, Fizmatlit, M., 2004, 59–112 | MR

[14] A. B. Ugolnikov, “O zamknutykh klassakh Posta”, Izv. vuzov. Matematika, 1988, no. 7(314), 79–88 | MR

[15] A. B. Ugolnikov, Klassy Posta, Izd-vo TsPI pri mekh.-mat. fak. MGU im. M. V. Lomonosova, M., 2008

[16] S. V. Yablonskii, Vvedenie v diskretnuyu matematiku, Vyssh. shk., M., 2006

[17] S. V. Yablonskii, “O klassakh funktsii algebry logiki, dopuskayuschikh prostuyu skhemnuyu realizatsiyu”, Uspekhi mat. nauk, 12:6(78) (1957), 189–196 | MR

[18] S. V. Yablonskii, “Ob algoritmicheskikh trudnostyakh sinteza minimalnykh kontaktnykh skhem”, Problemy kibernetiki, 1959, no. 2, 75–121

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

[20] Yu. I. Yanov, A. A. Muchnik, “O suschestvovanii $k$-znachnykh zamknutykh klassov, ne imeyuschikh konechnogo bazisa”, Dokl. AN SSSR, 127:1 (1959), 44–46

[21] E. L. Post, Two-valued iterative systems of mathematical logic, Annals of Math. Studies, 5, Princeton Univ. Press, Princeton–London, 1941 | MR