A relational approach to functional decomposition of logic circuits

Abstract

Functional decomposition of Boolean functions has a profound influence on all quality aspects of cost-effectively implementing modern digital systems and data-mining. The relational databases are multivalued tables, which include any truth tables of logic functions as special cases. In this article, we propose a relational database approach to the decomposition of logic circuits. The relational algebra consists of a set of well-defined algebraic operations that can be performed on multivalued tables. Our approach shows that the functional decomposition of logic circuits is similar to the normalization of relational databases; they are governed by the same concepts of functional dependency (FD) and multivalued dependency (MVD). The completeness of relational algebra demonstrated by our approach to functional decomposition reveals that the relational database is a fundamental computation model, the same as the Boolean logic circuit.