Emergent Mind
Substitutive systems and a finitary version of Cobham's theorem
(1908.11244)
Published Aug 29, 2019
in
math.CO
,
cs.FL
,
math.DS
,
and
math.NT
Abstract
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear as common factors of two automatic sequences defined over multiplicatively independent bases. This generalises the famous theorem of Cobham.
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