International Conference on Combinatorics on Words

WORDS 2015: Combinatorics on Words pp 1-13 | Cite as

Degrees of Transducibility

  • Jörg Endrullis
  • Jan Willem Klop
  • Aleksi Saarela
  • Markus Whiteland
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9304)


Our objects of study are infinite sequences and how they can be transformed into each other. As transformational devices, we focus here on Turing Machines, sequential finite state transducers and Mealy Machines. For each of these choices, the resulting transducibility relation \(\ge \) is a preorder on the set of infinite sequences. This preorder induces equivalence classes, called degrees, and a partial order on the degrees.

For Turing Machines, this structure of degrees is well-studied and known as degrees of unsolvability. However, in this hierarchy, all the computable streams are identified in the bottom degree. It is therefore interesting to study transducibility with respect to weaker computational models, giving rise to more fine-grained structures of degrees. In contrast with the degrees of unsolvability, very little is known about the structure of degrees obtained from finite state transducers or Mealy Machines.


Partial Order Turing Machine Infinite Sequence Finite Automaton Turing Degree 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jörg Endrullis
    • 1
  • Jan Willem Klop
    • 1
    • 2
  • Aleksi Saarela
    • 3
  • Markus Whiteland
    • 3
  1. 1.Department of Computer ScienceVU University AmsterdamAmsterdamThe Netherlands
  2. 2.Centrum Voor Wiskunde En Informatica (CWI)AmsterdamThe Netherlands
  3. 3.Department of Mathematics and Statistics and FUNDIMUniversity of TurkuTurkuFinland

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