Study of Nearly KK-MBF Type Functions

Recently, a special class of monotone Boolean functions (MBFs), known as the Kruskal-Katona class, arising from the theory of shadow minimization of finite set systems, was studied, and the deadlock-resolving set for these functions was determined.The zeros of KK-MBFs correspond to initial segments of the lexicographic order on layers of the binary cube; consequently, the units correspond to initial segments of the reverse-lexicographic order.In this paper, we extend the KK-MBF class by allowing a single unit (or a single zero) to appear at a specific location within the initial segment of the lexicographic (or reverse-lexicographic) order on the layers corresponding to the zeros (or units) of the function.