Geodesic
On the complexity of representation of $k$-valued functions by generalised polarised polynomials
Diskretnaya Matematika, Tome 21 (2009) no. 4, pp. 20-29.

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We consider generalised polarised polynomials for $k$-valued functions (for prime $k$). It is proved that each $k$-valued function is represented by some unique generalised polarised polynomial for each polarisation vector. We find upper and lower bounds for the Shannon functions of degree and length of the generalised polarised polynomials of $k$-valued functions. 
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S. N. Selezneva. On the complexity of representation of $k$-valued functions by generalised polarised polynomials. Diskretnaya Matematika, Tome 21 (2009) no. 4, pp. 20-29. http://geodesic.mathdoc.fr/item/DM_2009_21_4_a1/

[1] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Nauka, Moskva, 2001 | MR

[2] Peryazev N. A., “Slozhnost bulevykh funktsii v klasse polinomialnykh polyarizovannykh form”, Algebra i logika, 34:3 (1995), 323–326 | MR | Zbl

[3] Selezneva S. N., “O slozhnosti predstavleniya funktsii mnogoznachnykh logik polyarizovannymi polinomami”, Diskretnaya matematika, 14:2 (2002), 48–53 | MR | Zbl

[4] Kirichenko K. D., “Verkhnyaya otsenka slozhnosti polinomialnykh normalnykh form bulevykh funktsii”, Diskretnaya matematika, 17:3 (2005), 80–88 | MR | Zbl

[5] Selezneva S. N., Dainyak A. B., “O slozhnosti obobschennykh polinomov $k$-znachnykh funktsii”, Vestnik Moskovskogo Universiteta, ser. 15: vychisl. matem. i kibern., 2008, no. 3, 34–39 | MR

[6] Alekseev V. B., Voronenko A. A., Selezneva S. N., “O slozhnosti realizatsii funktsii $k$-znachnoi logiki polyarizovannymi polinomami”, Trudy V Mezhdunarodnoi konferentsii “Diskretnye modeli v teorii upravlyayuschikh sistem”, MGU, Moskva, 2003, 8–9

[7] Selezneva S. N., “O slozhnosti polyarizovannykh polinomov funktsii mnogoznachnykh logik, zavisyaschikh ot odnoi peremennoi”, Diskretnaya matematika, 16:2 (2004), 117–120 | MR | Zbl