On the Dynamic Qualitative Behaviour of Universal Computation

TL;DR

This paper investigates the relationship between a system's dynamic qualitative behaviour and its capacity for universal computation, proposing a compression-based measure and conjectures about Busy Beaver machines.

Contribution

It introduces a compression-based transition coefficient to quantify system sensitivity and explores the connection between qualitative behaviour and universality.

Findings

Proposes a new measure for system programmability

Formulates conjectures on Busy Beaver machines and universality

Highlights the importance of information transmission in computation

Abstract

We explore the possible connections between the dynamic behaviour of a system and Turing universality in terms of the system's ability to (effectively) transmit and manipulate information. Some arguments will be provided using a defined compression-based transition coefficient which quantifies the sensitivity of a system to being programmed. In the same spirit, a list of conjectures concerning the ability of Busy Beaver Turing machines to perform universal computation will be formulated. The main working hypothesis is that universality is deeply connected to the qualitative behaviour of a system, particularly to its ability to react to external stimulus--as it needs to be programmed--and to its capacity for transmitting this information.