DenseQMC: an efficient bit-slice implementation of the Quine-McCluskey algorithm

TL;DR

This paper introduces DenseQMC, an efficient bit-slice implementation of the Quine-McCluskey algorithm for dense Boolean functions, capable of handling up to 23-27 variables on standard hardware, and discusses common implementation mistakes.

Contribution

It presents DenseQMC, a novel optimized bit-slice implementation for the Quine-McCluskey algorithm, and corrects a widespread implementation error.

Findings

DenseQMC efficiently handles up to 23 variables on laptops.

It can process up to 27 variables on servers with 1 TiB RAM.

A common quadratic slowdown mistake is identified and corrected.

Abstract

This note describes a new efficient bit-slice implementation DenseQMC of the Quine-McCluskey algorithm for finding all prime implicants of a Boolean function in the dense case. It is practically feasible for n <= 23 when run on a common laptop or for n <= 27 when run on a server with 1 TiB RAM. This note also outlines a very common mistake in the implementations of the Quine-McCluskey algorithm, leading to a quadratic slowdown. An optimized corrected implementation of the classic approach is also given (called SparseQMC). The implementation is freely available at https://github.com/hellman/Quine-McCluskey .