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- W360848618 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]." @default.
- W360848618 created "2016-06-24" @default.
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- W360848618 date "2014-01-01" @default.
- W360848618 modified "2023-09-23" @default.
- W360848618 title "Eigenvalues and Transduction of Morphic Sequences" @default.
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- W360848618 doi "https://doi.org/10.1007/978-3-319-09698-8_21" @default.
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