Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-22T17:30:28.298Z Has data issue: false hasContentIssue false

A sharpening of the Parikh mapping

Published online by Cambridge University Press:  15 July 2002

Alexandru Mateescu
Faculty of Mathematics, University of Bucharest, Academiei 14, Bucharest, Romania; (
Arto Salomaa
Turku Centre for Computer Science, Lemminkäisenkatu 14, 20520 Turku, Finland; (
Kai Salomaa
Department of Computing and Information Science, Queen's University, Kingston, Ontario K7L 3N6, Canada; (
Sheng Yu
Department of Computer Science, University of Western Ontario, London, Ontario N6A 5B7, Canada; (
Get access


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 .

Research Article
© EDP Sciences, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


A. Atanasiu, C. Martín-Vide and A. Mateescu, On the injectivity of the Parikh matrix mapping (submitted).
T. Harju, O. Ibarra, J. Karhumäki and A. Salomaa, Some decision problems concerning semilinearity and commutation. J. Comput. System Sci. (to appear).
Honkala, J., On slender languages. EATCS Bull. 64 (1998) 145-152.
Honkala, J., Parikh, On slender languages and power series. J. Comput. System Sci. 52 (1996) 185-190. CrossRef
Ilie, L., An attempt to define mildly context-sensitive languages. Publ. Math. Debrecen 54 (1999) 865-876.
Ilie, L., Rozenberg, G. and Salomaa, A., A characterization of poly-slender context-free languages. RAIRO: Theoret. Informatics Appl. 34 (2000) 77-86.
Pansiot, J.J., A decidable property of iterated morphisms. Springer, Lecture Notes in Comput. Sci. 104 (1981) 152-158. CrossRef
Parikh, R.J., On context-free languages. J. Assoc. Comput. Mach. 13 (1966) 570-581. CrossRef
G. Rozenberg and A. Salomaa, Handbook of Formal Languages 1-3. Springer-Verlag, Berlin, Heidelberg, New York (1997).
J. Sakarovitch and I. Simon, Subwords, edited by M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, Mass. (1983) 105-142.
A. Salomaa, Formal Languages. Academic Press, New York (1973).