Predicting the large-scale evolution of tag systems

TL;DR

This paper introduces a predictive method for the large-scale evolution of tag systems based on their production rules, accurately forecasting growth and symbol distributions over multiple epochs.

Contribution

It develops a novel approach to predict tag system evolution by deriving symbol distributions across epochs, validated through comparison with simulations.

Findings

Predictions closely match simulation results over multiple epochs

The method accurately estimates growth rates and symbol densities

Effective for large-scale analysis of tag systems

Abstract

We present a method for predicting the large-scale evolution of a tag system from its production rules. A tag system's evolution is first divided into stages called `epochs' in which the tag system evolves monotonously. The distribution of symbols in the queue at the beginning of each epoch determines the tag system's large-scale properties, including growth rate and string densities, during that epoch. We derive the symbol distribution for the next epoch from the distribution for the current one, using this to make predictions over multiple successive epochs. Finally, we compare predictions that were obtained with this method to computer simulations and find that it retains great accuracy over several epochs.