English

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}
}