Threshold Function Identification by Redundancy Removal and Comprehensive Weight Assignments

Abstract

The identification of threshold function (TF), which determines whether a Boolean function can be represented by an linear threshold logic gate (LTG) or not, is a fundamental but important task in the theories of threshold logic. In this paper, we propose a more efficient and effective algorithm of TF identification by constructing the system of irredundant inequalities and adjusting the weight assignment comprehensively. This is the first non-ILP-based approach that is able to identify all the eight-input TFs. The experimental results demonstrated that the proposed approach is more effective than all the existing non-ILP-based approaches and the LTGs obtained by the proposed approach are optimal for near 100% cases. For TFs with 9–15 inputs, the proposed approach can identify 100 000 randomly generated TFs as well in a reasonable CPU time.