Shadow Minimization Boolean Function Reconstruction

A special class of monotone Boolean functions coming from shadow minimization theory of finite set -systems - KK-MBF functions - is considered. These functions are a descriptive model for systems of compatible groups of constraints, however, the class of all functions is unambiguously complex and it is sensible to study relatively simple subclasses of functions such as KK-MBF. Zeros of KK-MBF functions correspond to initial segments of lexicographic order on hypercube layers. This property is used to simplify the recognition. Lexicographic order applies priorities over constraints which is applicable property of practices. Query -based algorithms for KK-MBF functions are investigated in terms of their complexities.