Geodesic
On an upper bound for the cardinality of a~minimal teaching set of a~threshold function
Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 5, pp. 35-46.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new necessary and sufficient condition for belonging a point to a minimal teaching set of a threshold function of $k$-valued logic is proposed. This allows to extract a large subclass of threshold functions for which the cardinality of the minimal teaching set is bounded from above by a polynomial in $\log_k$ of degree $n-2$ when the number $n$ of variables is fixed. Ill. 1, bibliogr. 17.
Keywords: threshold function, teaching set, separation property. 
@article{DA_2012_19_5_a2,
     author = {N. Yu. Zolotykh and A. Yu. Chirkov},
     title = {On an upper bound for the cardinality of a~minimal teaching set of a~threshold function},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {35--46},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2012_19_5_a2/}
}
TY  - JOUR
AU  - N. Yu. Zolotykh
AU  - A. Yu. Chirkov
TI  - On an upper bound for the cardinality of a~minimal teaching set of a~threshold function
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2012
SP  - 35
EP  - 46
VL  - 19
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2012_19_5_a2/
LA  - ru
ID  - DA_2012_19_5_a2
ER  - 
%0 Journal Article
%A N. Yu. Zolotykh
%A A. Yu. Chirkov
%T On an upper bound for the cardinality of a~minimal teaching set of a~threshold function
%J Diskretnyj analiz i issledovanie operacij
%D 2012
%P 35-46
%V 19
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2012_19_5_a2/
%G ru
%F DA_2012_19_5_a2
N. Yu. Zolotykh; A. Yu. Chirkov. On an upper bound for the cardinality of a~minimal teaching set of a~threshold function. Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 5, pp. 35-46. http://geodesic.mathdoc.fr/item/DA_2012_19_5_a2/

[1] Veselov S. I., Chirkov A. Yu., “Otsenki chisla vershin tselykh poliedrov”, Diskret. analiz i issled. operatsii. Ser. 2, 14:2 (2007), 14–31 | MR | Zbl

[2] Virovlyanskaya M. A., Zolotykh N. Yu., “Verkhnyaya otsenka srednei moschnosti minimalnogo razreshayuschego mnozhestva porogovoi funktsii mnogoznachnoi logiki”, Vestn. Nizhegorodsk. gos. un-ta im. N. I. Lobachevskogoyu Matematicheskoe modelirovanie i optimalnoe upravlenie, 2003, no. 1, 238–246

[3] Virovlyanskaya M. A., Zolotykh N. Yu., “O moschnosti razreshayuschego mnozhestva porogovoi funktsii mnogoznachnoi logiki”, Mat. XIV Mezhdunar. shk.-seminara “Sintez i slozhnost upravlyayuschikh sistem”, Izd-vo Nizhegorodsk. gos. ped. un-ta, N. Novgorod, 2003, 20–21

[4] Zolotykh N. Yu., “O slozhnosti rasshifrovki porogovykh funktsii, zavisyaschikh ot dvukh peremennykh”, Mat. XI Mezhgos. shk.-seminara “Sintez i slozhnost upravlyayuschikh sistem”, Ch. I, Izd-vo Tsentra prikl. issled. pri mekh.-mat. fak. MGU, M., 2001, 74–79

[5] Zolotykh N. Yu., “Otsenki moschnosti minimalnogo razreshayuschego mnozhestva porogovoi funktsii mnogoznachnoi logiki”, Matematicheskie voprosy kibernetiki, 17, Fizmatlit, M., 2008, 159–168

[6] Zolotykh N. Yu., “Novaya modifikatsiya metoda dvoinogo opisaniya dlya postroeniya ostova mnogogrannogo konusa”, Zhurn. vychisl. matematiki i mat. fiziki, 52:1 (2012), 153–163 | MR | Zbl

[7] Zolotykh N. Yu., Shevchenko V. N., “Rasshifrovka porogovykh funktsii $k$-znachnoi logiki”, Diskret. analiz i issled. operatsii, 2:3 (1995), 18–23 | MR | Zbl

[8] Zolotykh N. Yu., Shevchenko V. N., “O nizhnei otsenke rasshifrovki porogovykh funktsii $k$-znachnoi logiki”, Zhurn. vychisl. matematiki i mat. fiziki, 39:2 (1999), 346–352 | MR | Zbl

[9] Skhreiver A., Teoriya lineinogo i tselochislennogo programmirovaniya, Mir, M., 1991, 360 pp. | MR

[10] Shevchenko V. N., “O chisle krainikh tochek v tselochislennom programmirovanii”, Kibernetika, 1981, no. 2, 133–134 | Zbl

[11] Shevchenko V. N., “O nekotorykh funktsiyakh mnogoznachnoi logiki, svyazannykh s tselochislennym programmirovaniem”, Metody diskretnogo analiza v teorii grafov i skhem, 42, In-t matematiki SO AN SSSR, Novosibirsk, 1985, 99–108 | MR

[12] Shevchenko V. N., Kachestvennye voprosy tselochislennogo programmirovaniya, Fizmatlit, M., 1995, 192 pp. | MR | Zbl

[13] Shevchenko V. N., Zolotykh N. Yu., “O slozhnosti rasshifrovki porogovykh funktsii $k$-znachnoi logiki”, Dokl. RAN, 362:5 (1998), 606–608 | MR | Zbl

[14] Antony M., Brightwell G., Shawe-Taylor J., “On exact specification by labeled examples”, Discrete Appl. Math., 61:1 (1995), 1–25 | DOI | MR

[15] Cook W., Hartmann M., Kannan R., McDiarmid C., “On integer points in polyhedra”, Combinatorica, 12:1 (1992), 27–37 | DOI | MR | Zbl

[16] Hegedüs T., “Geometrical concept learning and convex polytopes”, Proc. 7th Ann. ACM Conf. Computational Learning Theory (COLT' 94), ACM Press, New York, 1994, 228–236 | MR

[17] Hegedüs T., “Generalized teaching dimensions and the query complexity of learning”, Proc. 8th Ann. ACM Conf. Computational Learning Theory (COLT' 95), ACM Press, New York, 1995, 108–117