Two-Dimensional Digitized Picture Arrays and Parikh Matrices

Subramanian, K.G. and Mahalingam, Kalpana and Abdullah, Rosni and Nagar, Atulya K. (2013) Two-Dimensional Digitized Picture Arrays and Parikh Matrices. International Journal of Foundations of Computer Science, 24 (3). pp. 393-408. ISSN 1793-6373

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Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays A and B are defined to be M-equivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of M-ambiguity to a picture array. In the binary and ternary cases, conditions that ensure M-ambiguity are then obtained.

Item Type: Article
Additional Information and Comments: Electronic version of an article published as [International Journal of Foundations of Computer Science, 24, 3, 2013, 393-408] [10.1142/S012905411350010X] © [copyright World Scientific Publishing Company] [Journal URL]
Keywords: Word; subword; Parikh matrix; picture array; ambiguity
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty / Department: Faculty of Science > Mathematics and Computer Science
Depositing User: Users 3 not found.
Date Deposited: 05 Mar 2014 15:35
Last Modified: 22 Feb 2016 11:39

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