Mix-Automatic Sequences

  • Jörg Endrullis
  • Clemens Grabmayer
  • Dimitri Hendriks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7810)


Mix-automatic sequences form a proper extension of the class of automatic sequences, and arise from a generalization of finite state automata where the input alphabet is state-dependent. In this paper we compare the class of mix-automatic sequences with the class of morphic sequences. For every polynomial ϕ we construct a mix-automatic sequence whose subword complexity exceeds ϕ. This stands in contrast to automatic and morphic sequences which are known to have at most quadratic subword complexity. We then adapt the notion of k-kernels to obtain a characterization of mix-automatic sequences, and employ this notion to construct morphic sequences that are not mix-automatic.


Automatic Sequence Numeration System Finite State Automaton Number Format Input Alphabet 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jörg Endrullis
    • 1
  • Clemens Grabmayer
    • 2
  • Dimitri Hendriks
    • 1
  1. 1.VU University AmsterdamThe Netherlands
  2. 2.Utrecht UniversityThe Netherlands

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