Calculation of the minimum computational complexity based on information entropy

TL;DR

This paper introduces a method linking information entropy to the minimum computational complexity, providing a theoretical foundation for understanding the limits of problem-solving speed with computers.

Contribution

It establishes a novel relationship between information entropy and computational complexity, proposing a new perspective and rules for modeling problems in computational science.

Findings

Demonstrates the connection between entropy change and complexity

Provides examples illustrating the entropy-complexity relationship

Proposes a redefinition of information entropy in computational contexts

Abstract

In order to find out the limiting speed of solving a specific problem using computer, this essay provides a method based on information entropy. The relationship between the minimum computational complexity and information entropy change is illustrated. A few examples are served as evidence of such connection. Meanwhile some basic rules of modeling problems are established. Finally, the nature of solving problems with computer programs is disclosed to support this theory and a redefinition of information entropy in this filed is proposed. This will develop a new field of science.