On Infinite Words Determined by Indexed Languages

  • Tim Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8634)


We characterize the infinite words determined by indexed languages. An infinite language L determines an infinite word α if every string in L is a prefix of α. If L is regular or context-free, it is known that α must be ultimately periodic. We show that if L is an indexed language, then α is a morphic word, i.e., α can be generated by iterating a morphism under a coding. Since the other direction, that every morphic word is determined by some indexed language, also holds, this implies that the infinite words determined by indexed languages are exactly the morphic words. To obtain this result, we prove a new pumping lemma for the indexed languages, which may be of independent interest.


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© Springer-Verlag GmbH Berlin Heidelberg 2014

Authors and Affiliations

  • Tim Smith
    • 1
  1. 1.Northeastern UniversityBostonUSA

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