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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berstel, J., Perrin, D.: Theory of Codes. Academic Press, Orlando (1985)
Dömösi, P., Horváth, G.: The language of primitive words is not regular: Two simple proofs. Bulletin of the EATCS 87, 191–194 (2005)
Dömösi, P., Ito, M., Marcus, S.: Marcus contextual languages consisting of primitive words. Discrete Mathematics 308(21), 4877–4881 (2008)
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)
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)
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)
Dömösi, P., Horváth, S., Ito, M.: On the connection between formal languages and primitive words. Analele Univ. din Oradea, Fasc. Mat., 59–67 (1991)
Ginsburg, S.: The Mathematical Theory of Context-free Languages. McGraw-Hill, New York (1966)
Ginsburg, S., Spanier, E.H.: Bounded ALGOL-like languages. Trans. Am. Math. Soc. 113, 333–368 (1964)
Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978)
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)
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)
Ilie, L.: On a conjecture about slender context-free languages. Theoretical Computer Science 132(1-2), 427–434 (1994)
Ito, M., Katsura, M.: Context-free languages consisting of non-primitive words. Int. Journal of Computer Mathematics 40, 157–167 (1991)
Lothaire, M.: Combinatorics on Words. Encyclopedia of Mathematics and Its Applications, vol. 17. Addison-Wesley, Reading (1983)
Lothaire, M.: Algebraic Combinatorics on Words. In: Encyclopedia of Mathematics and Its Applications, vol. 90. Cambridge University Press, Cambridge (2002)
Petersen, H.: On the language of primitive words. Theoretical Computer Science 161, 141–156 (1996)
Shyr, H.: Free Monoids and Languages. Hon Min Book Company, Taichung (1991)
Shyr, H., Yu, S.: Non-primitive words in the language p + q + . Soochow J. Math. 4 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Leupold, P. (2010). Primitive Words Are Unavoidable for Context-Free Languages. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-13089-2_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13088-5
Online ISBN: 978-3-642-13089-2
eBook Packages: Computer ScienceComputer Science (R0)