Geodesic
Uniformity of a certain systems of functions of many-valued logic
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 61-64 
P. B. Tarasov. Uniformity of a certain systems of functions of many-valued logic. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 61-64. http://geodesic.mathdoc.fr/item/VMUMM_2013_2_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For any finite system $A$ of functions of many-valued logic taking values in the set $\{0,1\}$ such that a projection of $A$ generates the class of all monotone boolean functions, it is prooved that there exists constants $c$ and $d$ such that for an arbitrary function $f\in [A]$ the depth $D(f)$ and the complexity $L(f)$ of $f$ in the class of formulas over $A$ satisfy the relation $D(f)\leq c\log_2 L(f)+d$.

[1] Yablonskii S.V., Vvedenie v diskretnuyu matematiku, Vysshaya shkola, M., 2001 | MR

[2] Lau D., Function Algebras on Finite Sets, Springer-Verlag, Berlin–Heidelberg, 2006

[3] Ugolnikov A.B., “O glubine i polinomialnoi ekvivalentnosti formul dlya zamknutykh klassov dvuznachnoi logiki”, Matem. zametki, 42:4 (1987), 603–612 | MR

[4] Yablonskii S.V., Kozyrev V.P., “Matematicheskie voprosy kibernetiki”, Informatsionnye materialy Nauchnogo soveta po kompleksnoi probleme “Kibernetika” AN SSSR, 19 a, M., 1968, 3–15

[5] Spira R.M., “On time-hardware complexity tradeoffs for Boolean functions”, Proc. 4th Hawai Symposium on System Sciences, Western Periodicals Company, North Hollywood, 1971, 525–527

[6] Khrapchenko V.M., “O sootnoshenii mezhdu slozhnostyu i glubinoi formul”, Metody diskretnogo analiza v sinteze upravlyayuschikh sistem, 32, IM SO AN SSSR, Novosibirsk, 1978, 76–94 | MR

[7] Wegener I., “Relating monotone formula size and monotone depth of Boolean functions”, Inform. Proces. Let., 16 (1983), 41–42 | DOI | MR

[8] Ugolnikov A.B., “O sootnoshenii mezhdu glubinoi i slozhnostyu formul dlya zamknutykh klassov dvuznachnoi logiki”, IV Vsesoyuz. konf. “Primenenie metodov matematicheskoi logiki”, tez. dokl., Tallin, 1986, 184

[9] Ragaz M.E., “Parallelizable algebras”, Arch. fur math. Log. und Grundlagenforsch, 26 (1986/87), 77–99 | DOI | MR

[10] Safin R.F., “O glubine i slozhnosti formul v nekotorykh klassakh $k$-znachnoi logiki”, Vestn. Mosk. un-ta. Matem. Mekhan., 2000, no. 6, 65–68 | MR

[11] Safin R.F., “O sootnoshenii mezhdu glubinoi i slozhnostyu formul dlya predpolnykh klassov $k$-znachnoi logiki”, Matematicheskie voprosy kibernetiki, Fizmatlit, M., 2004, 223–278