Advertisement

Breadth-First Serialisation of Trees and Rational Languages

(Short Paper)
  • Victor Marsault
  • Jacques Sakarovitch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8633)

Abstract

We present here the notion of breadth-first signature of trees and of prefix-closed languages; and its relationship with numeration system theory. A signature is the serialisation into an infinite word of an ordered infinite tree of finite degree. Using a known construction from numeration system theory, we prove that the signature of (prefix-closed) rational languages are substitutive words and conversely that a special subclass of substitutive words define (prefix-closed) rational languages.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akiyama, S., Frougny, C., Sakarovitch, J.: Powers of rationals modulo 1 and rational base number systems. Israel J. Math. 168, 53–91 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Marsault, V., Sakarovitch, J.: Rhythmic generation of infinite trees and languages (2014), In preparation, early version accessible at arXiv:1403.5190Google Scholar
  3. 3.
    Rigo, M., Maes, A.: More on generalized automatic sequences. Journal of Automata, Languages and Combinatorics 7(3), 351–376 (2002)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Dumont, J.M., Thomas, A.: Systèmes de numŕation et fonctions fractales relatifs aux substitutions. Theor. Comput. Sci. 65(2), 153–169 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Cobham, A.: Uniform tag sequences. Math. Systems Theory 6, 164–192 (1972)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Diestel, R.: Graph Theory. Springer (1997)Google Scholar
  7. 7.
    Lecomte, P., Rigo, M.: Numeration systems on a regular language. Theory Comput. Syst. 34, 27–44 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Lecomte, P., Rigo, M.: Abstract numeration systems. In: Berthé, V., Rigo, M. (eds.) Combinatorics, Automata and Number Theory, pp. 108–162. Cambridge Univ. Press (2010)Google Scholar
  9. 9.
    Berthé, V., Rigo, M.: Combinatorics, Automata and Number Theory. Cambridge University Press (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Victor Marsault
    • 1
  • Jacques Sakarovitch
    • 1
  1. 1.Telecom-ParisTech and CNRSParisFrance

Personalised recommendations