A sharpening of the Parikh mapping

Alexandru Mateescu; Arto Salomaa; Kai Salomaa; Sheng Yu

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2001)

  • Volume: 35, Issue: 6, page 551-564
  • ISSN: 0988-3754

Abstract

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In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix product gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting interconnection between mirror images of words and inverses of matrices.

How to cite

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Mateescu, Alexandru, et al. "A sharpening of the Parikh mapping." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 35.6 (2001): 551-564. <http://eudml.org/doc/92684>.

@article{Mateescu2001,
abstract = {In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix product gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting interconnection between mirror images of words and inverses of matrices.},
author = {Mateescu, Alexandru, Salomaa, Arto, Salomaa, Kai, Yu, Sheng},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {formal languages; Parikh mapping; scattered subwords; Parikh vector},
language = {eng},
number = {6},
pages = {551-564},
publisher = {EDP-Sciences},
title = {A sharpening of the Parikh mapping},
url = {http://eudml.org/doc/92684},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Mateescu, Alexandru
AU - Salomaa, Arto
AU - Salomaa, Kai
AU - Yu, Sheng
TI - A sharpening of the Parikh mapping
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 6
SP - 551
EP - 564
AB - In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix product gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting interconnection between mirror images of words and inverses of matrices.
LA - eng
KW - formal languages; Parikh mapping; scattered subwords; Parikh vector
UR - http://eudml.org/doc/92684
ER -

References

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  1. [1] A. Atanasiu, C. Martín–Vide and A. Mateescu, On the injectivity of the Parikh matrix mapping (submitted). Zbl0997.68075
  2. [2] T. Harju, O. Ibarra, J. Karhumäki and A. Salomaa, Some decision problems concerning semilinearity and commutation. J. Comput. System Sci. (to appear). Zbl1059.68061MR1939772
  3. [3] J. Honkala, On slender languages. EATCS Bull. 64 (1998) 145-152. Zbl0898.68042MR1618305
  4. [4] J. Honkala, On Parikh slender languages and power series. J. Comput. System Sci. 52 (1996) 185-190. Zbl0846.68056MR1375813
  5. [5] L. Ilie, An attempt to define mildly context-sensitive languages. Publ. Math. Debrecen 54 (1999) 865-876. Zbl0981.68086MR1709927
  6. [6] L. Ilie, G. Rozenberg and A. Salomaa, A characterization of poly-slender context-free languages. RAIRO: Theoret. Informatics Appl. 34 (2000) 77-86. Zbl0966.68097MR1771131
  7. [7] J.J. Pansiot, A decidable property of iterated morphisms. Springer, Lecture Notes in Comput. Sci. 104 (1981) 152-158. Zbl0457.68095
  8. [8] R.J. Parikh, On context-free languages. J. Assoc. Comput. Mach. 13 (1966) 570-581. Zbl0154.25801MR209093
  9. [9] G. Rozenberg and A. Salomaa, Handbook of Formal Languages 1–3. Springer-Verlag, Berlin, Heidelberg, New York (1997). Zbl0866.68057
  10. [10] J. Sakarovitch and I. Simon, Subwords, edited by M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, Mass. (1983) 105-142. MR675953
  11. [11] A. Salomaa, Formal Languages. Academic Press, New York (1973). Zbl0262.68025MR438755

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