Geodesic
A rule for the addition of entropies for underdetermined data
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 5, pp. 67-90.

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The basic information characteristics for underdetermined data are introduced. For underdetermined data of the general form, it is proved that the entropy addition rule $H(X)+H(Y|X)=H(XY)$ of classic Information theory turns into a more complicated expression. The form of the expression is found. In addition, the necessary and sufficient conditions for it to coincide with the ordinary entropy addition rule are obtained. Bibliogr. 11.
Keywords: underdetermined data, information characteristics, entropy, conditional entropy, specification, best specification, entropy addition rule. 
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L. A. Sholomov. A rule for the addition of entropies for underdetermined data. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 5, pp. 67-90. http://geodesic.mathdoc.fr/item/DA_2010_17_5_a6/

[1] Bongard M. M., “O ponyatii ‘poleznaya informatsiya’ ”, Probl. kibernetiki, 9, Fizmatgiz, M., 1963, 71–102

[2] Gallager R., Teoriya informatsii i nadezhnaya svyaz, Sov. radio, M., 1974, 720 pp. | Zbl

[3] Kolmogorov A. N., Algoritm, informatsiya, slozhnost, Znanie, M., 1991, 48 pp. | MR | Zbl

[4] Sholomov L. A., “Informatsionnye svoistva funktsionalov slozhnosti dlya sistem nedoopredelënnykh bulevykh funktsii”, Probl. kibernetiki, 34, Nauka, M., 1978, 133–150 | MR

[5] Sholomov L. A., “Szhatie chastichno opredelënnoi informatsii”, Nelineinaya dinamika i upravlenie, 4, Fizmatlit, M., 2004, 385–399

[6] Sholomov L. A., “O mere informatsii nechëtkikh i chastichno-opredelënnykh dannykh”, Dokl. RAN, 410:3 (2006), 321–325 | MR | Zbl

[7] Sholomov L. A., “Ob effektivnom postroenii protykayuschikh mnozhestv”, Vestn. TGU, 2007, Pril. No 23, 68–74 | MR

[8] Sholomov L. A., “Obobschënnoe pravilo slozheniya entropii dlya nedoopredelënnykh dannykh”, Dokl. RAN, 427:1 (2009), 28–31 | MR | Zbl

[9] Andreev A. E., Complexity of nondeterministic functions, BRICS report series RS-94-2, February 1994, 47 pp.

[10] Andreev A. E., Clementi A. E. F., Rolim J. D. P., “Hitting sets derandomize BPP”, Automata, languages and programming, 23rd Int. Colloquium (Paderborn, Germany, 1996), Lect. Notes Comp. Sci., 1099, Springer-Verl., Berlin, 1996, 357–368 | MR | Zbl

[11] Linial L., Luby M., Saks M., Zuckerman D., “Efficient construction of a small hitting set for combinatorial rectangles in high dimension”, Combinatorica, 17 (1997), 215–234 | DOI | MR | Zbl