SAT is a problem with exponential complexity measured by negentropy

TL;DR

This paper explores how negentropy can measure computational complexity, demonstrating that SAT has exponential complexity and supporting the NP!=P conjecture through analysis of specific problems.

Contribution

It introduces negentropy as a measure of complexity and applies it to analyze SAT, providing evidence for its exponential complexity and implications for P vs NP.

Findings

SAT has exponential complexity based on negentropy analysis

Logical compare and sorting have lower complexities

Supports NP!=P conjecture

Abstract

In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of computation and information was clearly stated. Then the complexities of three specific problems: logical compare, sorting and SAT, were analyzed and measured. The result showed SAT was a problem with exponential complexity which naturally leads to the conclusion that no efficient algorithm exists to solve it. That's to say: NP!=P.