The Computational Complexity of Classical Knot Recognition

TL;DR

This paper investigates the computational difficulty of identifying whether a given knot diagram represents a classical knot, establishing its NP membership and providing an exponential time decision algorithm.

Contribution

It proves that classical knot recognition is in NP and introduces an exponential time algorithm for the problem.

Findings

Knot recognition problem is in NP.

An exponential time algorithm for knot recognition.

Provides theoretical bounds for the problem.

Abstract

The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.