Computing with Coloured Tangles

TL;DR

This paper introduces a diagrammatic computational model using coloured tangles, demonstrating Turing completeness and the ability to decide IP class languages with potential efficiency advantages over classical methods.

Contribution

It presents a novel diagram-based computation framework inspired by topology, proving Turing completeness and efficiency in complexity class IP.

Findings

Model is Turing complete

Can decide IP class languages

Potentially better performance than classical protocols

Abstract

We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of computation is Turing complete, and that with bounded resources it can moreover decide any language in complexity class IP, sometimes with better performance parameters than corresponding classical protocols.