no. 6
A sharpening of the Parikh mapping
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 6, pp. 551-564

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.

Classification : 68Q45, 68Q70
Keywords: formal languages, Parikh mapping, scattered subwords 
@article{ITA_2001__35_6_551_0,
     author = {Mateescu, Alexandru and Salomaa, Arto and Salomaa, Kai and Yu, Sheng},
     title = {A sharpening of the {Parikh} mapping},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {551--564},
     year = {2001},
     publisher = {EDP Sciences},
     volume = {35},
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     mrnumber = {1922295},
     zbl = {1005.68092},
     language = {en},
     url = {https://www.numdam.org/item/ITA_2001__35_6_551_0/}
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Mateescu, Alexandru; Salomaa, Arto; Salomaa, Kai; Yu, Sheng. A sharpening of the Parikh mapping. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 6, pp. 551-564. https://www.numdam.org/item/ITA_2001__35_6_551_0/

[1] A. Atanasiu, C. Martín-Vide and A. Mateescu, On the injectivity of the Parikh matrix mapping (submitted). | Zbl

[2] T. Harju, O. Ibarra, J. Karhumäki and A. Salomaa, Some decision problems concerning semilinearity and commutation. J. Comput. System Sci. (to appear). | Zbl | MR

[3] J. Honkala, On slender languages. EATCS Bull. 64 (1998) 145-152. | Zbl | MR

[4] J. Honkala, On Parikh slender languages and power series. J. Comput. System Sci. 52 (1996) 185-190. | Zbl | MR

[5] L. Ilie, An attempt to define mildly context-sensitive languages. Publ. Math. Debrecen 54 (1999) 865-876. | Zbl | MR

[6] L. Ilie, G. Rozenberg and A. Salomaa, A characterization of poly-slender context-free languages. RAIRO: Theoret. Informatics Appl. 34 (2000) 77-86. | Zbl | MR | Numdam

[7] J.J. Pansiot, A decidable property of iterated morphisms. Springer, Lecture Notes in Comput. Sci. 104 (1981) 152-158. | Zbl

[8] R.J. Parikh, On context-free languages. J. Assoc. Comput. Mach. 13 (1966) 570-581. | Zbl | MR

[9] G. Rozenberg and A. Salomaa, Handbook of Formal Languages 1-3. Springer-Verlag, Berlin, Heidelberg, New York (1997). | Zbl

[10] J. Sakarovitch and I. Simon, Subwords, edited by M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, Mass. (1983) 105-142. | MR

[11] A. Salomaa, Formal Languages. Academic Press, New York (1973). | Zbl | MR