Scattered Context-Free Linear Orderings

  • Zoltán Ésik
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.


Linear Ordering Lexicographic Order Exponential Time Primitive Root Strong Component 
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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)MathSciNetzbMATHGoogle 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)MathSciNetCrossRefzbMATHGoogle 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)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ésik, Z.: An undecidable property of context-free linear orders. Information Processing Letters 111, 107–109 (2001)CrossRefzbMATHGoogle Scholar
  10. 10.
    Lothaire, M.: Combinatorics on Words. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle 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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