Undecidability and Finite Automata

  • Jörg Endrullis
  • Jeffrey ShallitEmail author
  • Tim Smith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10396)


Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to prove the undecidability of a related problem about k-automatic sets of rational numbers.


Finite automata Undecidability Conjugate Power 



We thank Hendrik Jan Hoogeboom and the referees for their helpful comments.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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