Scattered Context-Free Linear Orderings

  • Zoltán Ésik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)


We show that it is decidable in exponential time whether the lexicographic ordering of a context-free language is scattered, or a well-ordering.


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  1. 1.
    Blum, N., Koch, R.: Greibach normal form transformation. Information and Computation 150, 112–118 (1999) (revisited)Google Scholar
  2. 2.
    Braud, L., Carayol, A.: Linear orders in the pushdown hierarchy. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 88–99. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Bloom, S.L., Ésik, Z.: Regular and Algebraic Words and Ordinals. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds.) CALCO 2007. LNCS, vol. 4624, pp. 1–15. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Bloom, S.L., Ésik, Z.: Algebraic ordinals. Fundamenta Informaticæ 99, 383–407 (2010)MathSciNetMATHGoogle Scholar
  5. 5.
    Bloom, S.L., Ésik, Z.: Algebraic linear orderings. In: Int. J. Foundations of Computer Science (to appear)Google Scholar
  6. 6.
    Caucal, D.: On infinite graphs having a decidable monadic theory. Theoretical Computer Science 290, 79–115 (2003)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Ésik, Z.: Algebraic and context-free linear orderings. Slides Presented at, Workshop on Higher-Order Recursion Schemes & Pushdown Automata, Paris, March 10–12 (2010),
  8. 8.
    Ésik, Z., Iván, S.: Büchi context-free languages. Theoretical Computer Science 412, 805–821 (2011)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Ésik, Z.: An undecidable property of context-free linear orders. Information Processing Letters 111, 107–109 (2001)CrossRefMATHGoogle Scholar
  10. 10.
    Lothaire, M.: Combinatorics on Words. Cambridge University Press, Cambridge (1997)CrossRefMATHGoogle Scholar
  11. 11.
    Rosenstein, J.G.: Linear Orderings. Pure and Applied Mathematics, vol. 98. Academic Press, New York (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Zoltán Ésik
    • 1
  1. 1.Department of InformaticsUniversity of SzegedSzegedHungary

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