Conway's cosmological theorem and automata theory
Formal Languages and Automata Theory
2025-11-24 v1
Abstract
John Conway proved that every audioactive sequence (a.k.a. look-and-say) decays into a compound of 94~elements, a statement he termed the cosmological theorem. The underlying audioactive process can be modeled by a finite-state machine, mapping one sequence of integers to another. Leveraging automata theory, we propose a new proof of Conway's theorem based on a few simple machines, using a computer to compose and minimize them.
Keywords
Cite
@article{arxiv.2409.20341,
title = {Conway's cosmological theorem and automata theory},
author = {Pierre Lairez and Aleksandr Storozhenko},
journal= {arXiv preprint arXiv:2409.20341},
year = {2025}
}