A Reduced Offset Based Method for Fast Computation of the Prime Implicants Covering a Given Cube

TL;DR

This paper introduces a novel reduced offset method utilizing bitwise operations for faster, more memory-efficient computation of prime implicants, improving both speed and quality over traditional minimization techniques.

Contribution

The paper proposes a reduced offset concept based on positional-cube representation to address exponential complexity in prime implicant generation, enabling faster and more efficient minimization.

Findings

Significantly speeds up the minimization process

Improves the quality of prime implicants

Reduces memory requirements for computation

Abstract

In order to generate prime implicants for a given cube (minterm), most of minimization methods increase the dimension of this cube by removing one literal from it at a time. But there are two problems of exponential complexity. One of them is the selection of the order in which the literals are to be removed from the implicant at hand. The latter is the mechanism that checks whether a tentative literal removal is acceptable. The reduced Offset concept has been developed to avoid of these problems. This concept is based on positional-cube representation where each cube is represented by two n-bit strings. We show that each reduced Off-cube may be represented by a single n-bit string and propose a set of bitwise operations to be performed on such strings. The experiments on single-output benchmarks show that this approach can significantly speed up the minimization process, improve the quality of its results and reduce the amount of memory required for this aim.