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Eigenvalues and Transduction of Morphic Sequences

  • David Sprunger
  • William Tune
  • Jörg Endrullis
  • Lawrence S. Moss
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8633)

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].

Keywords

Incidence Matrix Dominant Eigenvalue Input Alphabet Morphic Image Output Alphabet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • David Sprunger
    • 1
  • William Tune
    • 1
  • Jörg Endrullis
    • 1
    • 2
  • Lawrence S. Moss
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Department of Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands

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