On the Injectivity of the Parikh Matrix Mapping
نویسندگان
چکیده
In this paper we investigate the injectivity of the Parikh matrix mapping. This research is done mainly on the binary alphabet. We identify a family of binary words, refered to as “palindromicly amicable”, such that two such words are palindromicly amicable if and only if they have the same image by the Parikh matrix mapping. Some other related problems are discussed, too.
منابع مشابه
Parikh Matrices and Parikh Rewriting Systems
Since the introduction of the Parikh matrix mapping, its injectivity problem is on top of the list of open problems in this topic. In 2010 Salomaa provided a solution for the ternary alphabet in terms of a Thue system with an additional feature called counter. This paper proposes the notion of a Parikh rewriting system as a generalization and systematization of Salomaa’s result. It will be show...
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1. A. Atanasiu. Binary amiable words. International Journal of Foundations of Computer Science, 18(2):387–400, 2007. 2. A. Atanasiu, R. Atanasiu, and I. Petre. Parikh matrices and amiable words. Theoretical Computer Science, 390:102–109, 2008. 3. A. Atanasiu, C. Martin-Vide, and A. Mateescu. On the injectivity of the parikh matrix mapping. Fundamenta Informatica, 46:1–11, 2001. 4. S. Bera and K...
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We deal with the notion of M-unambiguity [5] in connection with the Parikh matrix mapping introduced by Mateescu and others in [7]. M-unambiguity is studied both in terms of words and matrices and several sufficient criteria for M-unambiguity are provided in both cases, nontrivially generalizing the criteria based on the γ-property introduced by Salomaa in [15]. Also, the notion of M-unambiguit...
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We introduce an extension of the Parikh mapping called the Parikh -matrix mapping, which takes its values in matrices with polynomial entries. The morphism constructed represents a word over a -letter alphabet as a -dimensional upper-triangular matrix with entries that are nonnegative integral polynomials in variable . We show that by appropriately embedding the -letter alphabet into the -lette...
متن کاملA q-Matrix Encoding Extending the Parikh Matrix Mapping
We introduce a generalization of the Parikh mapping called the Parikh q-matrix encoding, which takes its values in matrices with polynomial entries. The encoding represents a word w over a k-letter alphabet as a (k + 1)-dimensional upper-triangular matrix with entries that are nonnegative integral polynomials in variable q. Putting q = 1, we obtain the morphism introduced by Mateescu, Salomaa, ...
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عنوان ژورنال:
- Fundam. Inform.
دوره 49 شماره
صفحات -
تاریخ انتشار 2002