The computational complexity of Kauffman nets and the P versus NP problem

TL;DR

This paper explores how adjusting parameters in Kauffman nets affects the difficulty of finding their global energy minima, with implications for physics and the P versus NP problem.

Contribution

It demonstrates that small changes in problem parameters can drastically alter problem complexity, offering new insights into computational hardness and potential approaches to P versus NP.

Findings

Parameter adjustments cause extreme sensitivity in problem difficulty

Implications for physics of random systems

Potential strategies for P versus NP

Abstract

Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model can be adjusted so that the problem of finding its global energy minimum is extremely sensitive to small changes in the problem statement. This result has implications not only for studies of the physics of random systems but may also lead to new strategies for resolving the well-known P versus NP question in computational complexity theory.