Multi-output, multi-level, multi-gate design using non-linear programming

TL;DR

This paper introduces a non-linear programming approach for minimizing multi-output Boolean functions using any two-input gates, guaranteeing minimal solutions and handling incompletely specified functions.

Contribution

It presents a novel non-linear mixed integer programming method that ensures minimality and flexibility in Boolean function minimization beyond traditional gate sets.

Findings

Achieves equal or better minimization results compared to existing methods.

Guarantees minimal solutions for Boolean function minimization.

Handles incompletely specified Boolean functions effectively.

Abstract

Using logic gates is the traditional way of designing logic circuits. However, most of the minimization algorithms concern a limited set of gates (complete sets), like sum of products, exclusive-or sum of products, NAND gates, NOR gates e.t.c.. In this paper, a method is proposed for minimizing multi-output Boolean functions using any kind of two-input gates although it can easily be extended to multi-input gates. The method is based on non-linear mixed integer programming. The experimental results show that the method gives the same or better results compared to other methods available in the literature. However, other methods do not ensure that they produce the minimal solution, while the main advantages of the proposed method are that it does guarantee minimality and it can also handle Boolean functions for incompletely specified functions. The method is general enough and can easily be extended to more complicated design modules than just basic gates.