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A sharpening of the Parikh mapping

Alexandru Mateescu, Arto Salomaa, Kai Salomaa, Sheng Yu
2001 RAIRO - Theoretical Informatics and Applications  
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.  ...  As already pointed out, the Parikh matrix mapping gives more information about a word than the classical Parikh mapping, although the Parikh matrix mapping is still not injective.  ... 
doi:10.1051/ita:2001131 fatcat:k6xqvcmhxjgstlozmp5a2xta5m

On Generalized Parikh Matrices for Finite and Infinite Words

Huldah Samuel
2013 International Journal of Computer Applications  
The concept of the Generalized Parikh Matrices (GPM) of words is introduced in this paper. Some results and properties of the GPM for finite words over  are discussed.  ...  The definition is extended for infinite words too.  ...  An extension of the Parikh mapping, called the Parikh matrix mapping was introduced in [3] based on a certain type of matrices.  ... 
doi:10.5120/11658-7175 fatcat:3ezasbgz35f5peusxfgo2bw2xi

Extending Parikh q-matrices

Somnath Bera, Kalpana Mahalingam
2016 International Journal of Computer Applications  
Also it has been shown that the extending Parikh q-matrix mapping can be obtained as a composition of a Parikh q-matrix mapping and a word substitution morphism.  ...  The notion of extending Parikh q-matrix with respect to a word instead of an ordered alphabet is introduced. Some basic properties of this extending Parikh q-matrices have been investigated.  ...  Acknowledgements This research was partially supported by the Department of Science and Technology, India (MAT/15-16/046/DSTX/KALP) awarded to Dr.Kalpana Mahalingam.  ... 
doi:10.5120/ijca2016907909 fatcat:z2cjkbehqfbetmxjmgtoxal6w4

Parikh Matrices and Istrail Morphism

K.G. Subramanian, Pradeep Isawasan, Ibrahim Venkat
2013 Malaysian Journal of Fundamental and Applied Sciences  
ACKNOWLEDGEMENT The authors would like to thank the reviewers for their useful comments. The authors gratefully acknowledge support for this research from  ...  in ; and the rightmost entry in the first row gives the number of subwordabc's in w.The Parikh matrix is known [5, 7] to be not injective which means that two or more words can have the same Parikh matrix  ...  Recently, Parikh mapping has been extended in [5] by introducing the concept of a Parikh matrix mapping or Parikh matrix, which gives more numerical information than a Parikh vector does.  ... 
doi:10.11113/mjfas.v9n1.72 fatcat:cp7wz6b6ajfovl6yalt6s3uhzi

ON PARIKH MATRICES

K. G. SUBRAMANIAN, ANG MIIN HUEY, ATULYA K. NAGAR
2009 International Journal of Foundations of Computer Science  
The Parikh matrix gives more information than the well-known Parikh vector of a word which counts only occurrences of symbols in a word.  ...  Thus the ratio property gives information on the M −ambiguity of certain words and certain sets of words.  ...  The first two authors gratefully acknowledge support for this research by a short term grant of the Universiti Sains Malaysia.  ... 
doi:10.1142/s0129054109006528 fatcat:pehu6xc7ufdx7m3ompft3oq3wy

Independence of certain quantities indicating subword occurrences

Arto Salomaa
2006 Theoretical Computer Science  
According to the main result in this paper, no entry in a Parikh matrix, no matter how high the dimension, can be computed in terms of the other entries.  ...  The numerical quantity investigated in this paper is |w| u , the number of occurrences of a word u as a (scattered) subword of a word w.  ...  Acknowledgements The useful suggestions of two referees are gratefully acknowledged. In particular, the second referee sharpened the proof of Lemma 3.  ... 
doi:10.1016/j.tcs.2006.06.025 fatcat:p3cckqjtxjhijgsuuh6h577asm

Connections between subwords and certain matrix mappings

Arto Salomaa
2005 Theoretical Computer Science  
Parikh matrices recently introduced have turned out to be a powerful tool in the arithmetizing of the theory of words.  ...  This paper continues the investigation of Parikh matrices and subword occurrences.  ...  Acknowledgements The author is grateful to the referee for useful suggestions.  ... 
doi:10.1016/j.tcs.2005.03.024 fatcat:uh25jsbjqfhivekwpssmyqg7ui

On M-ambiguity of Words corresponding to a Parikh Matrix

Amrita Bhattacharjee
2017 International Journal of Computer Applications  
M-ambiguous words are the problem of Parikh matrix. In this paper an algorithm is introduced to find the M-ambiguous ternary words corresponding to a 4x4 matrix.  ...  The concept of M-ambiguity Reduction factor is introduced. With the help of this M-ambiguity Reduction factor the problem of Mambiguity can be solved to some extent.  ...  Parikh matrix of a word gives much more information about a word than Parikh vector. But Parikh Matrix faces some challenging problems, such as it is not injective.  ... 
doi:10.5120/ijca2017915439 fatcat:2ubxlir37zeitnod6jfhn4d3sm

Parikh Matrices and Words over Tertiary Ordered Alphabet

Amrita Bhattacharjee, Bipul Syam Purkayastha
2014 International Journal of Computer Applications  
A set of equations for finding tertiary words from the respective Parikh matrix is introduced. These equations are useful to find tertiary words from the respective Parikh matrix. Examples are given.  ...  Parikh matrix is a numerical property of a word on an ordered alphabet. It is used for studying word in terms of its sub words. It was introduced by Mateescu et al. in 2000.  ...  From these equations one can find the word corresponding to a 5x5 Parikh matrix. Parikh Matrix faces some challenging problems. The most important of them is that it is not injective.  ... 
doi:10.5120/14827-3069 fatcat:duuwjv3zavgb7jvwo42pqbnn4e

Some Alternative Ways to Find M-Ambiguous Binary Words Corresponding to a Parikh Matrix

Amrita Bhattacharjee, Bipul Syam Purkayastha
2014 International Journal on Computational Science & Applications  
With the help of this algorithm Parikh matrix of a binary word, however large it may be can be found out. M-ambiguous words are the problem of Parikh matrix.  ...  Parikh matrix of a word gives numerical information of the word in terms of its subwords. In this Paper an algorithm for finding Parikh matrix of a binary word is introduced.  ...  As such Parikh Matrix of a word gives information about Parikh vector of the same. Parikh Matrix still faces some challenging problems, such as it is not injective.  ... 
doi:10.5121/ijcsa.2014.4106 fatcat:zh4rr32znvgmfmyxvn4vvysxli

TWO-DIMENSIONAL DIGITIZED PICTURE ARRAYS AND PARIKH MATRICES

K. G. SUBRAMANIAN, KALPANA MAHALINGAM, ROSNI ABDULLAH, ATULYA K. NAGAR
2013 International Journal of Foundations of Computer Science  
Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word.  ...  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.  ...  Acknowledgement The comments of the reviewers have been of great help in revising the paper and to make a better presentation of the ideas.  ... 
doi:10.1142/s012905411350010x fatcat:jzvtj4hb4bhblceeqocrgadvw4

Subword histories and Parikh matrices

Alexandru Mateescu, Arto Salomaa, Sheng Yu
2004 Journal of computer and system sciences (Print)  
Parikh matrices recently introduced give much more information about a word than just the number of occurrences of each letter.  ...  In this paper we introduce the closely related notion of a subword history and obtain a sequence of general results: elimination of products, decidability of equivalence, and normal form.  ...  The Parikh matrix mapping is not injective even for the alphabet fa; bg: For instance, consider the matrices 1 4 6 0 1 3 0 0 1 0 B @ 1 C A and 1 5 8 0 1 3 0 0 1 0 B @ 1 C A: Then the five words baabaab  ... 
doi:10.1016/j.jcss.2003.04.001 fatcat:62dqhugqnbdlvg4mvmiwfpxhg4

Strong 2.t and Strong 3.t Transformations for Strong M-equivalence [article]

Ghajendran Poovanandran, Wen Chean Teh
2017 arXiv   pre-print
Due to the dependency of Parikh matrices on the ordering of the alphabet, strong M-equivalence was proposed as an order-independent alternative to M-equivalence in studying words possessing the same Parikh  ...  matrix.  ...  Injectivity of the Parikh matrix mappings revisited. Fund. Inform., 73(1):265–283, 2006. [17] W. C. Teh. On core words and the Parikh matrix mapping. Internat. J. Found. Comput.  ... 
arXiv:1702.03647v1 fatcat:2f246jalejfste6y6h6ebuaxcy

Reducing the Ambiguity of Parikh Matrices [chapter]

Jeffery Dick, Laura K. Hutchinson, Robert Mercaş, Daniel Reidenbach
2020 Lecture Notes in Computer Science  
The Parikh matrix mapping allows us to describe words using matrices. Although compact, this description comes with a level of ambiguity since a single matrix may describe multiple words.  ...  More specifically, for any word, we study the Parikh matrix of its Lyndon conjugate as well as that of its projection to a smaller alphabet.  ...  The bulk of the work done on the Parikh matrix mapping concerns the ambiguity that Parikh matrices exhibit.  ... 
doi:10.1007/978-3-030-40608-0_28 fatcat:btqhbzqvtngt3aftjkru2mzche

PARIKH MATRICES, AMIABILITY AND ISTRAIL MORPHISM

ADRIAN ATANASIU
2010 International Journal of Foundations of Computer Science  
Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of words having the same Parikh matrix; these words are called "amiable" or  ...  The morphism proposed here is the Istrail morphism.  ...  Acknowledgments I would like to thank the anonymous referees for their valuable comments and useful remarks about this paper.  ... 
doi:10.1142/s0129054110007702 fatcat:wworrm3dmnbx5o4lnuovuudfyq
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