Degrees of Infinite Words, Polynomials and Atoms

  • Jörg Endrullis
  • Juhani Karhumäki
  • Jan Willem Klop
  • Aleksi Saarela
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)


Our objects of study are finite state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite automata for recognising and transforming languages are well-understood, very little is known about the power of automata to transform infinite words.

We use methods from linear algebra and analysis to show that there is an infinite number of atoms in the transducer degrees, that is, minimal non-trivial degrees.


Turing Machine Finite Automaton Weighted Product Turing Degree Infinite Word 
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-Verlag Berlin Heidelberg 2016

Authors and Affiliations

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

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