A Relational Approach to Functional Decomposition of Logic Circuits

TL;DR

This paper introduces a relational approach to logic circuit decomposition, inspired by database normalization, using bipartite graphs to represent dependencies and improve cost-effective digital system design.

Contribution

It presents a novel method linking logic circuit decomposition with relational database concepts through bipartite graph representations.

Findings

Bipartite graphs effectively model functional dependencies in logic circuits.

Algorithms constructed from these graphs meet information-lossless criteria.

The approach parallels database normalization principles.

Abstract

Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is proposed. This approach is parallel to the normalization of relational databases, they are governed by the same concepts of functional dependency (FD) and multi-valued dependency (MVD). It is manifest that the functional decomposition of switching function actually exploits the same idea and serves a similar purpose as database normalization. Partitions play an important role in the decomposition. The interdependency of two partitions can be represented by a bipartite graph. We demonstrate that both FD and MVD can be represented by bipartite graphs with specific topological properties, which are delineated by partitions of minterms. It follows that our algorithms are procedures of constructing those specific bipartite graphs of interest to meet the information-lossless criteria of functional decomposition.