A SHORT PROOF OF A THEOREM OF COBHAM ON SUBSTITUTIONS

This paper is concerned with the lengths of constant length substitutions that generate topologically conjugate systems. We show that if the systems are infinite, then these lengths must be powers of the same integer. This result is a dynamical formulation of a special case of a 1969 theoretical com...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2014-01, Vol.44 (1), p.19-22
Main Authors: COVEN, ETHAN M., DYKSTRA, ANDREW, LEMASURIER, MICHELLE
Format: Article
Language:English
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Summary:This paper is concerned with the lengths of constant length substitutions that generate topologically conjugate systems. We show that if the systems are infinite, then these lengths must be powers of the same integer. This result is a dynamical formulation of a special case of a 1969 theoretical computer science result of Cobham [1]. Our proof is rather simple.
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-2014-44-1-19