On extendibility of unavoidable sets

  • Christian Choffrut
  • Karel CulikII
Contibuted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)


A subset X of a free monoid A is said to be unavoidable if all but finitely many words in A contain some word of X as a subword. A. Ehrenfeucht has conjectured that every unavoidable set X is extendible in the sense that there exist x ε X and a ε A such that (X-{x}) ∪ {xa} is itself unavoidable. This problem remains open, we give some partial solutions and show how to efficiently test unavoidability, extendibility and other properties of X related to the problem.


State Diagram Infinite Sequence Empty Word Free Monoid Extendible Element 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Christian Choffrut
    • 1
  • Karel CulikII
    • 2
  1. 1.Laboratoire d'Informatique Théorique et ProgrammationUniversité Paris VIIParisFrance
  2. 2.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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