Abstract
We study finite state transduction of automatic and morphic sequences. Dekking [4] 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 α-substitutivity. Roughly, a sequence is α-substitutive if the sequence can be obtained as the limit of iterating a substitution with dominant eigenvalue α. Our results culminate in the following fact: for multiplicatively independent real numbers α and β, if v is a α-substitutive sequence and w is an β-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 [5].
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Sprunger, D., Tune, W., Endrullis, J., Moss, L.S. (2014). Eigenvalues and Transduction of Morphic Sequences. In: Shur, A.M., Volkov, M.V. (eds) Developments in Language Theory. DLT 2014. Lecture Notes in Computer Science, vol 8633. Springer, Cham. https://doi.org/10.1007/978-3-319-09698-8_21
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DOI: https://doi.org/10.1007/978-3-319-09698-8_21
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