Advertisement

Primitive Words Are Unavoidable for Context-Free Languages

  • Peter Leupold
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)

Abstract

We introduce the concept of unavoidability of languages with respect to a language class; this means that every language of the given class shares at least some word with the unavoidable language. Several examples of such unavoidabilities are presented. The most interesting one is that the set of primitive words is unavoidable for context-free languages that are not linear.

Keywords

Regular Language Analogous Reasoning Primitive Root Language Class Formal Language Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berstel, J., Perrin, D.: Theory of Codes. Academic Press, Orlando (1985)zbMATHGoogle Scholar
  2. 2.
    Dömösi, P., Horváth, G.: The language of primitive words is not regular: Two simple proofs. Bulletin of the EATCS 87, 191–194 (2005)zbMATHGoogle Scholar
  3. 3.
    Dömösi, P., Ito, M., Marcus, S.: Marcus contextual languages consisting of primitive words. Discrete Mathematics 308(21), 4877–4881 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Dömösi, P., Martín-Vide, C., Mitrana, V.: Remarks on sublanguages consisting of primitive words of slender regular and context-free languages. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds.) Theory Is Forever. LNCS, vol. 3113, pp. 60–67. Springer, Heidelberg (2004)Google Scholar
  5. 5.
    Dömösi, P., Hauschildt, D., Horváth, G., Kudlek, M.: Some results on small context-free grammars generating primitive words. Publicationes Mathematicae Debrecen 54, 667–686 (1999)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Dömösi, P., Horváth, G., Ito, M.: A small hierarchy of languages consisting of non-primitive words. Publicationes Mathematicae Debrecen 64(3-4), 261–267 (2004)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Dömösi, P., Horváth, S., Ito, M.: On the connection between formal languages and primitive words. Analele Univ. din Oradea, Fasc. Mat., 59–67 (1991)Google Scholar
  8. 8.
    Ginsburg, S.: The Mathematical Theory of Context-free Languages. McGraw-Hill, New York (1966)zbMATHGoogle Scholar
  9. 9.
    Ginsburg, S., Spanier, E.H.: Bounded ALGOL-like languages. Trans. Am. Math. Soc. 113, 333–368 (1964)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978)zbMATHGoogle Scholar
  11. 11.
    Horváth, S., Ito, M.: Decidable and undecidable problems of primitive words, regular and context-free languages. Journal of Universal Computer Science 5(9), 532–541 (1999)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Horváth, S., Leupold, P., Lischke, G.: Roots and powers of regular languages. In: Ito, M., Toyama, M. (eds.) DLT 2002. LNCS, vol. 2450, pp. 220–230. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Ilie, L.: On a conjecture about slender context-free languages. Theoretical Computer Science 132(1-2), 427–434 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ito, M., Katsura, M.: Context-free languages consisting of non-primitive words. Int. Journal of Computer Mathematics 40, 157–167 (1991)zbMATHCrossRefGoogle Scholar
  15. 15.
    Lothaire, M.: Combinatorics on Words. Encyclopedia of Mathematics and Its Applications, vol. 17. Addison-Wesley, Reading (1983)zbMATHGoogle Scholar
  16. 16.
    Lothaire, M.: Algebraic Combinatorics on Words. In: Encyclopedia of Mathematics and Its Applications, vol. 90. Cambridge University Press, Cambridge (2002)Google Scholar
  17. 17.
    Petersen, H.: On the language of primitive words. Theoretical Computer Science 161, 141–156 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Shyr, H.: Free Monoids and Languages. Hon Min Book Company, Taichung (1991)zbMATHGoogle Scholar
  19. 19.
    Shyr, H., Yu, S.: Non-primitive words in the language p  +  q  + . Soochow J. Math. 4 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Peter Leupold
    • 1
  1. 1.Fachbereich Elektrotechnik/Informatik, Fachgebiet Theoretische InformatikUniversität KasselKasselGermany

Personalised recommendations