A Heuristic Approach to Two Level Boolean Minimization Derived from Karnaugh Mapping

TL;DR

This paper introduces a heuristic method for simplifying sum-of-product Boolean expressions, focusing on removing redundant prime implicants, which scales better than traditional methods like Karnaugh maps and Quine-McCluskey for complex expressions.

Contribution

A novel heuristic approach derived from Boolean laws and Karnaugh mapping that improves scalability in Boolean minimization.

Findings

Reduces computational complexity compared to traditional methods.

Effectively simplifies large Boolean expressions.

Focuses on removing redundant prime implicants.

Abstract

The following paper presents a heuristic method by which sum-of-product Boolean expressions can be simplified with a specific focus on the removal of redundant and selective prime implicants. Existing methods, such as the Karnaugh map and the Quine-McCluskey method [1, 2], fail to scale since they increase exponentially in complexity as the quantity of literals increases, doing as such to ensure the solution is algorithmically obtained. By employing a heuristic model, nearly all expressions can be simplified at an overall reduction in computational complexity. This new method was derived from the fundamental Boolean laws, Karnaugh mapping, as well as truth tables.