Conway's cosmological theorem and automata theory
Abstract
John Conway proved that every audioactive sequence (a.k.a. \emph{look-and-say}) decays into a compound of 94~elements, a statement he termed the \emph{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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