A Note on Generic Tangle Algorithms

TL;DR

This paper summarizes three fundamental algorithms for identifying and certifying tangles within abstract separation systems, providing theoretical insights into their operation and interrelations.

Contribution

It presents a theoretical overview of three basic tangle algorithms, including a naive search, a certificate generator, and a tree-of-tangles construction.

Findings

Provides a theoretical framework for tangle algorithms

Details an algorithm for certifying non-existence of tangles

Describes a method to construct a tree-of-tangles

Abstract

In this note we gather the theoretical outlines of three basic algorithms for tangles in abstract separation systems: a naive tree search for finding tangles; an algorithm which outputs a certificate for the non-existence of tangles if possible, and otherwise a way to jump-start the naive tree search; and a way to obtain a tree-of-tangles.