Conway's cosmological theorem and automata theory

TL;DR

This paper provides a new automata-theoretic proof of Conway's cosmological theorem, demonstrating that the look-and-say sequence ultimately decomposes into 94 fundamental elements, using finite-state machines and computational minimization.

Contribution

It introduces a novel automata-based proof of Conway's theorem, employing simple machines and computer-assisted minimization techniques.

Findings

Confirmed the decay of look-and-say sequences into 94 elements

Developed a new automata-theoretic proof method

Utilized computer algorithms for machine composition and minimization

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.