An undecidable property of context-free linear orders

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We prove that there exists no algorithm to decide whether the language generated by a context-free grammar is dense with respect to the lexicographic ordering. As a corollary to this result, we show that it is undecidable whether the lexicographic orderings of the languages generated by two context-free grammars have the same order type.

Original languageEnglish
Pages (from-to)107-109
Number of pages3
JournalInformation Processing Letters
Issue number3
Publication statusPublished - Jan 1 2011



  • Context-free language
  • Decidability
  • Formal languages
  • Lexicographic ordering

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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