Geodesic
On the complexity of decoding Boolean cube splitting into cube faces
Diskretnaya Matematika, Tome 20 (2008) no. 2, pp. 46-62.

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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. 
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     title = {On the complexity of decoding {Boolean} cube splitting into cube faces},
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V. V. Osokin. On the complexity of decoding Boolean cube splitting into cube faces. Diskretnaya Matematika, Tome 20 (2008) no. 2, pp. 46-62. http://geodesic.mathdoc.fr/item/DM_2008_20_2_a4/

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