Convex Continuation of a Boolean Functionand Its Applications

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Convex Continuation of a Boolean Functionand Its Applications

Barotov, D N

Journal of applied and industrial mathematics, 01/2024, Volume: 18, Issue: 1

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A convex continuation of an arbitrary Boolean function to the set is constructed. Moreover, it is proved that for any Boolean function that has no neighboring points on the set , the constructed function is the only totally maximally convex continuation to . Based on this, in particular, it is constructively stated that the problem of solving an arbitrary system of Boolean equations can be reduced to the problem of minimizing a function any local minimum of which in the desired region is a global minimum, and thus for this problem the problem of local minima is completely resolved.

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