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On the complexity of decoding Boolean cube splitting into cube faces. (English. Russian original) Zbl 1192.68230
Discrete Math. Appl. 18, No. 2, 155-172 (2008); translation from Diskretn. Mat. 20, No. 2, 46-62 (2008).
Summary: We consider the known problem of decoding functions of Boolean algebra, that is, we need to completely restore the table of values of a function defined on an \(n\)-dimensional Boolean cube \(B^{n}\) using its values on some subset of \(B^{n}\). If the function belongs to some narrower class than the class of all functions of \(n\) variables (for example, to the set of monotone or threshold functions), then only vectors of a subset of \(n\)-dimensional Boolean cube can be required to completely determine the function. In the paper, we consider the class of functions which split the \(n\)-dimensional Boolean cube into cube faces. An asymptotic estimate for complexity of decoding functions that belong to any subclass of this class with fixed structure is obtained.

MSC:
68P20 Information storage and retrieval of data
68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)
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References:
[1] Deerwester S., J. Amer. Soc. Information Sci. 41 pp 391– (1990)
[2] Papadimitriou C. H., J. Comput. Syst. Sci. 61 pp 217– (2000) · Zbl 0963.68063
[3] Korobkov V. K., Probl. Cybern. 13 pp 5– (1965)
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