Sierpinski Gaskets for Logic Functions Representation

TL;DR

This paper presents a novel method of representing logic functions using Sierpinski Gaskets, leveraging their recursive fractal structure to improve logic design and minimization processes.

Contribution

It introduces a new fractal-based representation for logic functions and explores its applications in logic minimization and decision diagram enhancement.

Findings

Enhanced logic function minimization techniques.

Potential improvements in decision diagram representations.

Experimental validation on benchmark problems.

Abstract

This paper introduces a new approach to represent logic functions in the form of Sierpinski Gaskets. The structure of the gasket allows to manipulate with the corresponding logic expression using recursive essence of fractals. Thus, the Sierpinski gasket's pattern has myriad useful properties which can enhance practical features of other graphic representations like decision diagrams. We have covered possible applications of Sierpinski gaskets in logic design and justified our assumptions in logic function minimization (both Boolean and multiple-valued cases). The experimental results on benchmarks with advances in the novel structure are considered as well.