On complexity measures of complexes of faces in the unit cube

Under study is the problem of proving the minimality of complexes of faces in the unit cube. Basing on the ordinal properties of a complexity measure functional and the structural properties of Boolean functions, we formulated some sufficient conditions that can be used to prove that a complex of faces is minimal. This allowed us to expand the set of complexes of faces that were proved to be minimal with respect to the complexity measures with certain properties. The strict inclusion is proved for the sets of complexes of faces: kernel, minimal for an arbitrary complexity measure, and minimal for every complexity measure that is invariant under replacement of faces with isomorphic faces.