Eigenvalues and Transduction of Morphic Sequences: Extended Version
Abstract
We study finite state transduction of automatic and morphic sequences. Dekking proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in the proof to show that non-erasing transductions preserve a condition called alpha-substitutivity. Roughly, a sequence is alpha-substitutive if the sequence can be obtained as the limit of iterating a substitution with dominant eigenvalue alpha. Our results culminate in the following fact: for multiplicatively independent real numbers alpha and beta, if v is an alpha-substitutive sequence and w is a beta-substitutive sequence, then v and w have no common non-erasing transducts except for the ultimately periodic sequences. We rely on Cobham's theorem for substitutions, a recent result of Durand.
Keywords
Cite
@article{arxiv.1406.1754,
title = {Eigenvalues and Transduction of Morphic Sequences: Extended Version},
author = {David Sprunger and William Tune and Jörg Endrullis and Lawrence S. Moss},
journal= {arXiv preprint arXiv:1406.1754},
year = {2014}
}