Geodesic
Test recognition
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 4, pp. 67-99.

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

We describe the logic approach to pattern recognition; its key notion is a test. Analyzing the tests allows us to construct functional characterizing the pattern, as well as procedures to compute them. We present qualitative and quantitative properties of tests, functionals, and recognition procedures. Solutions of a series of known problems are also given. 
@article{FPM_2009_15_4_a3,
     author = {V. B. Kudryavtsev and A. E. Andreev},
     title = {Test recognition},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {67--99},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_4_a3/}
}
TY  - JOUR
AU  - V. B. Kudryavtsev
AU  - A. E. Andreev
TI  - Test recognition
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2009
SP  - 67
EP  - 99
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2009_15_4_a3/
LA  - ru
ID  - FPM_2009_15_4_a3
ER  - 
%0 Journal Article
%A V. B. Kudryavtsev
%A A. E. Andreev
%T Test recognition
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2009
%P 67-99
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2009_15_4_a3/
%G ru
%F FPM_2009_15_4_a3
V. B. Kudryavtsev; A. E. Andreev. Test recognition. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 4, pp. 67-99. http://geodesic.mathdoc.fr/item/FPM_2009_15_4_a3/

[1] Andreev A. E., O kachestvennykh i metricheskikh svoistvakh testovykh algoritmov, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1981 | MR

[2] Dolotova O. A., O slozhnosti kontrolya logicheskikh skhem tipa Posta, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1991

[3] Dyukova E. V., Asimptoticheski optimalnye testovye algoritmy v zadachakh raspoznavaniya, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1979

[4] Zhuravlëv Yu. I., “Ob algebraicheskom podkhode k resheniyu zadach raspoznavaniya i klassifikatsii”, Problemy kibernetiki, 31, 1978, 5–68

[5] Kibkalo A. A., O $T$-algoritmakh raspoznavaniya, ispolzuyuschikh korotkie testy, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1988

[6] Konstantinov R. M., Korolëva Z. E., Kudryavtsev V. B., “Kombinatorno-logicheskii podkhod k zadacham prognoza rudonosnosti”, Problemy kibernetiki, 31, 1976, 25–41

[7] Krendelev F. P., Dmitriev A. N., Zhuravlëv Yu. I., “Sravnenie geologicheskogo stroeniya zarubezhnykh mestorozhdenii dokembriiskikh konglomeratov s pomoschyu diskretnoi matematiki”, DAN SSSR, 173:5 (1967), 1149–1152

[8] Kuznetsov V. E., “Ob odnom stokhasticheskom algoritme vychisleniya informatsionnykh kharakteristik tablits po metodu testov”, Diskret. analiz, 23, 1973, 8–23 | Zbl

[9] Nefidov F. N., Postroenie modeli lecheniya detei s nekotorymi ostrymi zabolevaniyami bryushnoi polosti, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1977

[10] Noskov V. N., “O slozhnosti testov, kontroliruyuschikh rabotu vkhodov logicheskikh skhem”, Mat. zametki, 18:1 (1975), 137–150 | MR | Zbl

[11] Nosov M. V., Funktsionalnye kharakteristiki testovykh algoritmov raspoznavaniya obrazov, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1989

[12] Pereyaslavskii V. V., Dis. $\dots$ kand. fiz.-mat. nauk, M., 1958

[13] Pogosyan G. R., O slozhnosti proveryayuschikh testov dlya logicheskikh ustroistv, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1982

[14] Slepyan V. A., “Parametry raspredeleniya tupikovykh testov i informatsionnye vesa stolbtsov v binarnykh tablitsakh”, Diskret. analiz, 14, 1969, 28–43 | Zbl

[15] Solovev N. A., Testy (teoriya, postroenie, primenenie), Nauka, Novosibirsk, 1978 | MR

[16] Chegis I. A., Yablonskii S. V., “Logicheskie sposoby kontrolya elektricheskikh skhem”, Tr. Mat. in-ta im. V. A. Steklova, 51, 1958, 270–360 | MR | Zbl

[17] Shaieb A., Issledovanie svoistv lineinykh metricheskikh algoritmov raspoznavaniya, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1958

[18] Yablonskii S. V., Gavrilov G. P., Kudryavtsev V. B., Funktsii algebry logiki i klassy Posta, Nauka, M., 1966 | MR