The algorithm for completeness recognizing in function algebra~$L(\mathbb Z)$

A. I. Mamontov ; D. G. Meshchaninov

Diskretnaya Matematika, Tome 26 (2014) no. 1, pp. 85-95.

Bibliographie

[1] Darsaliya V. Sh., “Usloviya polnoty dlya polinomov s naturalnymi, tselymi i ratsionalnymi koeffitsientami”, Fundam. i prikl. matem., 2:2 (1996), 365–374 | MR | Zbl

[2] Darsaliya V. Sh., “Ob algoritmicheskoi razreshimosti svoistva vyrazimosti dlya polinomov”, Fundam. i prikl. matem., 5:3 (1999), 931–935 | MR | Zbl

[3] Darsaliya V. Sh., “Otnositelnaya polnota dlya funktsionalnykh sistem polinomov”, Fundam. i prikl. matem., 8:4 (2002), 967–977 | MR | Zbl

[4] Mamontov A. I., Meschaninov D. G., “Problema polnoty v funktsionalnoi sisteme lineinykh polinomov s tselymi koeffitsientami”, Trudy VI Mezhdunar. konf. “Diskretnye modeli v teorii upravlyayuschikh sistem”, Izd. otdel f-ta VMiK MGU, Moskva, 2004, 50–52

[5] Mamontov A. I., Meschaninov D. G., “Problema polnoty v funktsionalnoi sisteme lineinykh polinomov s tselymi koeffitsientami”, Diskretnaya matematika, 22 (2010), 64–82 | DOI | MR | Zbl

[6] Meschaninov D. G., Nikitin I. V., “Funktsionalno zamknutye klassy polinomov, sokhranyayuschikh nekotorye ekvivalentnosti na chislovykh mnozhestvakh”, Vestnik MEI, 2011, no. 6, 14–23

[7] Meschaninov D. G., Nikitin I. V., “Klassy sokhraneniya porogovykh razbienii v funktsionalnykh sistemakh polinomov”, Vestnik MEI, 2012, no. 6, 132–141

[8] Alekseev V. B., Emelyanov N. R., “Metod postroeniya bystrykh algoritmov v $k$-znachnoi logike”, Matem. zametki, 38:1 (1985), 148–156 | MR | Zbl

[9] Emelyanov N. R., “Ob odnom podkhode k postroeniyu effektivnykh algoritmov raspoznavaniya polnoty v mnogoznachnykh logikakh”, Matem. zametki, 39:5 (1986), 766–775 | MR | Zbl

[10] Selezneva S. N., “O slozhnosti raspoznavaniya polnoty mnozhestv bulevykh funktsii, realizovannykh polinomami Zhegalkina”, Diskretnaya matematika, 9:4 (1997), 24–31 | DOI | MR | Zbl

[11] Selezneva S. N., “O slozhnosti raspoznavaniya polnoty sistem funktsii $k$-znachnoi logiki, zadannykh polinomami”, Trudy VI Mezhdunar. konf. “Diskretnye modeli v teorii upravlyayuschikh sistem”, Izd. otdel f-ta VMiK MGU, Moskva, 2004, 76–79

[12] Gorshkov S. P., “O slozhnosti raspoznavaniya multiaffinnosti, biyunktivnosti, slaboi polozhitelnosti i slaboi otritsatelnosti bulevykh funktsii”, Obozr. prikl. i promyshl. matem., 4:2 (1997), 216–237

[13] Selezneva S. N., “Polinomialnyi algoritm dlya raspoznavaniya prinadlezhnosti realizovannoi polinomom funktsii $k$-znachnoi logiki predpolnym klassam samodvoistvennykh funktsii”, Diskretnaya matematika, 10:3 (1998), 64–72 | DOI | MR | Zbl

[14] Voronenko A. A., “On the complexity of monotonicity verification”, Proc. 15-th Ann. IEEE Conf. Comput. Complexity, Florence, 1999, 235–238 | MR

[15] Selezneva S. N., “Polinomialnyi algoritm dlya raspoznavaniya prinadlezhnosti funktsii $k$-znachnoi logiki, predstavlennykh polinomami, k predpolnym klassam lineinykh funktsii”, Vestnik MGU. Ser 15: Vych. matem. i kibern., 2001, no. 3, 40–43 | MR | Zbl

[16] Vyalyi M. N., “Algoritmicheskie zadachi s tablitsami znachenii bulevykh polinomov”, Trudy ISP RAN, 6, 2004, 51–64

[17] Bukhman A. V., “O slozhnosti raspoznavaniya sokhraneniya funktsiyami mnogoznachnykh logik, zadannykh polinomami, nekotorykh mnozhestv”, Vestnik MGU. Ser. 15: Vych. matem. i kibernetika, 2011, no. 3, 38–43 | MR | Zbl

[18] Bukhman A. V., “Polinomialnyi algoritm raspoznavaniya funktsii, invariantnykh otnositelno preobrazovaniya Mëbiusa”, Materialy XI Mezhdunar. sem. “Diskretnaya matematika i ee prilozheniya”, Izd-vo mekh.-mat. f-ta MGU, Moskva, 2012, 188–190

[19] Bukhman A. V., “O primenenii obobschennykh polinomov dlya postroeniya algoritmov raspoznavaniya svoistv $k$-znachnykh funktsii, zadannykh polinomami”, Diskretnaya matematika, 24:3 (2012), 51–61 | DOI | MR | Zbl

[20] Slupecki J., “Kryterium pelnosci wielowar-tosciowych systemóv logiki zdań”, Comptes Rendus des Séances de la Société des Siences et de Lettres de Varsovie. Cl. III, 32 (1939), 102–109

[21] Yablonskii S. V., “Funktsionalnye postroeniya v $k$-znachnoi logike”, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, 51, 1958, 5–142 | MR | Zbl

[22] Salomaa A., “Nekotorye kriterii polnoty dlya mnozhestv funktsii mnogoznachnoi logiki”, Kibern. sb., 8, 1964, 7–32

[23] Gavrilov G. P., “O funktsionalnoi polnote v schetnoznachnoi logike”, Probl. kibern., 15, 1965, 5–64 | MR | Zbl

[24] Mamontov A. I., “Problema otnositelnoi polnoty v funktsionalnoi sisteme lineinykh polinomov s ratsionalnymi koeffitsientami”, Vestnik MEI, 2011, no. 6, 133–142

[25] Koblits N., Kurs teorii chisel i kriptografii, TVP, Moskva, 2001