9-Input Threshold Function Identification Using a New Necessary Condition of Threshold Function

Identification of a threshold function (TF) is a significant task that determines whether a given Boolean function is a TF or not. The state-of-the-art only identifies all 8-input NP-class TFs. In this article, we propose a new necessary condition for a function being a representative NP-class TF. With the proposed necessary condition, we design an effective approach to identify 9-input NP-class TFs. As a result, we reduce the candidate set of 9-input functions being TFs to an extremely tiny subset of all 9-input Boolean functions. Experimental results show that our approach successfully identifies at least 80% of 9-input NP-class TFs. This is the first attempt to deal with this challenging problem in the literature.