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arXiv · 2409.20341

Conway's cosmological theorem and automata theory

Pierre Lairez·Aleksandr Storozhenko
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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.

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Pierre Lairez, Aleksandr Storozhenko. 2024-09-30. Conway's cosmological theorem and automata theory. https://doi.org/10.1080/00029890.2025.2549225

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