On approximation of continuous functions by determinate functions with delay
Diskretnaya Matematika, Tome 22 (2010) no. 1, pp. 83-103.

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We consider determinate functions with delay which are extensions of determinate functions and find some properties of these functions. The problem is posed to approximate continuous functions by functions with delay, and the assertion is proved that it is possible to approximate any continuous function with an arbitrary accuracy. Approximations for some functions are given, including the addition and multiplication functions which are minimal from the delay viewpoint.
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A. N. Cherepov. On approximation of continuous functions by determinate functions with delay. Diskretnaya Matematika, Tome 22 (2010) no. 1, pp. 83-103. http://geodesic.mathdoc.fr/item/DM_2010_22_1_a6/

[1] Kolmogorov A. N., “O predstavlenii nepreryvnykh funktsii neskolkikh peremennykh v vide superpozitsii nepreryvnykh funktsii odnogo peremennogo”, Dokl. AN SSSR, 114:5 (1957), 953–956 | MR | Zbl

[2] Kudryavtsev V. B., Aleshin S. V., Podkolzin A. S., Vvedenie v teoriyu avtomatov, Nauka, 1985 | MR | Zbl

[3] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, Moskva, 1974 | MR

[4] Ofman Yu., “Ob algoritmicheskoi slozhnosti diskretnykh funktsii”, Dokl. AN SSSR, 145:1 (1962), 48–51 | MR | Zbl

[5] Ofman Yu., “O priblizhennoi realizatsii nepreryvnykh funktsii na avtomatakh”, Dokl. AN SSSR, 152:4 (1963), 823–826 | MR | Zbl

[6] Tyulenev N. F., “Priblizhenie nepreryvnykh funktsii diskretnymi”, Trudy seminara po diskretnoi matematike i ee prilozheniyam, Izd-vo mekh.-mat. f-ta MGU, Moskva, 1997, 148–151

[7] Tyulenev N. F., “O priblizhenii nepreryvnykh funktsii diskretnymi”, Konstruktsii v algebre i logike, Tverskoi gos. universitet, Tver, 1990, 110–116 | MR

[8] Cherepov A. N., Cherepov I. A., “O predstavlenii nedeterminirovannykh funktsii determinirovannymi”, Tez. dokl. XIII Mezhdunarodnoi konf. “Problemy teoreticheskoi kibernetiki”, v. 2, Izd-vo mekh.-mat. f-ta MGU, Moskva, 2002, 191

[9] Cherepov A. N., Cherepov I. A., “O klassifikatsii nedeterminirovannykh funktsii”, Trudy seminara po diskretnoi matematike i ee prilozheniyam, Izd-vo mekh.-mat. f-ta MGU, Moskva, 2004, 160–163

[10] Cherepov A. N., “O slozhnosti priblizheniya nepreryvnykh funktsii nedeterminirovannymi funktsiyami s zaderzhkoi”, Materialy IX Mezhdunarodnoi konf. “Intellektualnye sistemy i kompyuternye nauki”, v. 1(2), Izd-vo mekh.-mat. f-ta MGU, Moskva, 2006, 307–310

[11] Cherepov I. A., “O priblizhenii nepreryvnykh funktsii determinirovannymi funktsiyami s zaderzhkoi”, Trudy seminara po diskretnoi matematike i ee prilozheniyam, Izd-vo mekh.-mat. f-ta MGU, Moskva, 2004, 163–166

[12] Trakhtenbrot B. A., “Ob operatorakh, realizuemykh v logicheskikh setyakh”, Dokl. AN SSSR, 112:6 (1957), 1005–1007

[13] Trakhtenbrot B. A., “Konechnye avtomaty i logika odnomestnykh predikatov”, Sibirskii matem. zhurnal, 3:1 (1962), 103–131 | Zbl

[14] Trakhtenbrot B. A., Barzdin Ya. M., Konechnye avtomaty (povedenie i sintez), Nauka, Moskva, 1970 | MR | Zbl

[15] Burks A. W., Wright J. B., “Theory of logical nets”, Proc. IRE, 41 (1953), 1357–1365 | DOI | MR | Zbl

[16] Bernhardt L., Lindner R., Thiele H., “Über sequentiell berechenbare reelle Abbildungen”, Elektron. Inform.-Verarb. Kybernetik, 7 (1971), 317–329 | MR | Zbl

[17] Valk R., “Topologische Wortmengen, topologische Automaten, zustandsendliche, stetige Abbildungen”, Mitteilungen der Gesellschaft für Mathematik und Datenverarbeitung, 19, GMD, Bonn, 1972, 133–135