TY - JOUR
T1 - Conway’s Cosmological Theorem and Automata Theory
AU - Lairez, Pierre
AU - Storozhenko, Aleksandr
N1 - Publisher Copyright:
© 2025 The Mathematical Association of America.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/105016691550
U2 - 10.1080/00029890.2025.2549225
DO - 10.1080/00029890.2025.2549225
M3 - Article
AN - SCOPUS:105016691550
SN - 0002-9890
VL - 132
SP - 867
EP - 882
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 9
ER -