Conquering Uncertainty in Multiple-Valued Logic Design

Abstract

In modern science, significant advances are typically made at cross-roads of disciplines. Thus, many optimization problems in Multiple-valued Logic Design have been successfully approached using ideas and techniques from Artificial Intelligence. In particular, improvements in multiple-valued logic design have been made by exploiting information/uncertainty measures. In this paper, we review well-known information measures in the multiple-valued domain and consider some methods of finding information measures for completely or incompletely specified functions with multiple-valued and continuous attributes. In this respect, the paper addresses the problem known as discretization and introduces a method of finding an optimal representation of continuous data in the multiple-valued domain. We also propose a technique for efficient calculation of different information measures using Multiple-valued Decision Diagrams. As one application of our technique, we outline an approach to synthesizing digital circuits derived from decision diagrams that can yield to reduction in power dissipation. The paper also shows the impact in several important areas of multiple-valued system design including (i) fuzzy logic, (ii) quantum computing systems, and (iii) data mining.