Interior and exterior functions of positive Boolean functions

The interior function and exterior function of a Boolean function f are introduced [14] in order to express its stability and robustness properties. In this paper, we investigate the complexity of two problems -INTERIOR and -EXTERIOR. We rst answer the question about the complexity of -INTERIOR left open in [14]; it has no polynomial total time algorithm even if is bounded by a constant, unless P=NP. However, for positive h-term DNF functions with h bounded by a constant, problem -INTERIOR and -EXTERIOR can be solved in (input) polynomial time and polynomial delay, respectively. Furthermore, for positive k-DNF functions, -INTERIOR for two cases in which k = 1, and and k are both bounded by a constant, can be solved in polynomial delay and in polynomial time, respectively. 3 Department of Systems and Human Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan. ([email protected]) y Department of Applied Mathematics and Physics..