Coding Partitions: Regularity, Maximality and Global Ambiguity

  • Marie-Pierre Béal
  • Fabio Burderi
  • Antonio Restivo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4588)


The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences.

We firstly prove that the canonical coding partition of a regular set contains a finite number of regular classes. We give an algorithm for computing this partition. We then investigate maximality conditions in a coding partition and we prove, in the regular case, the equivalence between two different notions of maximality. As an application, we finally derive some new properties of maximal uniquely decipherable codes.


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  1. 1.
    Béal, M.-P., Perrin, D.: Codes, unambiguous automata and sofic systems. Theoret. Comput. Sci. 356, 6–13 (2006)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Berstel, J., Perrin, D.: Theory of codes, Orlando, FL. Pure and Applied Mathematics, vol. 117. Academic Press Inc, San Diego (1985), MATHGoogle Scholar
  3. 3.
    Burderi, F., Restivo, A.: Coding partitions, Discret. Math. Theor. Comput. Sci (to appear)Google Scholar
  4. 4.
    Dalai, M., Leonardi, R.: Non prefix-free codes for constrained sequences. In: ISIT 2005. International Symposium on Information Theory, pp. 1534–1538. IEEE, New York (2005)CrossRefGoogle Scholar
  5. 5.
    Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press, New York (1974)MATHGoogle Scholar
  6. 6.
    Gönenç, G.: Unique decipherability of codes with constraints with application to syllabification of Turkish words. In: COLING 1973: Computational And Mathematical Linguistics: Proceedings of the International Conference on Computational Linguistics, vol. 1, pp. 183–193 (1973)Google Scholar
  7. 7.
    Guzmán, F.: Decipherability of codes. J. Pure Appl. Algebra 141, 13–35 (1999)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Karhumäki, W.P.J., Rytter, W.: Generalized factorizations of words and their algorithmic properties. Theoret. Comput. Sci. 218, 123–133 (1999)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Lempel, A.: On multiset decipherable codes. IEEE Trans. Inform. Theory 32, 714–716 (1986)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Restivo, A.: A note on multiset decipherable codes. IEEE Trans. Inform. Theory 35, 662–663 (1989)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Sakarovitch, J.: Éléments de théorie des automates, Vuibert, Paris. Cambridge University Press, Cambridge (English translation to appear) (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Marie-Pierre Béal
    • 1
  • Fabio Burderi
    • 2
  • Antonio Restivo
    • 2
  1. 1.Institut Gaspard-Monge, Laboratoire d’informatique UMR 8049, Université de Marne-la-Vallée, 77454 Marne-la-Vallée Cedex 2France
  2. 2.Dipartimento di Matematica ed Applicazioni, Università degli studi di Palermo, Via Archirafi 34, 90123 PalermoItaly

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