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- W304996000 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." @default.
- W304996000 created "2016-06-24" @default.
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- W304996000 date "2014-06-05" @default.
- W304996000 modified "2023-09-27" @default.
- W304996000 title "Eigenvalues and Transduction of Morphic Sequences: Extended Version." @default.
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