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Two – Dimensional Grammars Based on Patterns

Christopher Kezia Parimalam1 , J.D. Emerald2

Section:Research Paper, Product Type: Journal Paper
Volume-07 , Issue-05 , Page no. 216-220, Mar-2019

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v7si5.216220

Online published on Mar 10, 2019

Copyright © Christopher Kezia Parimalam, J.D. Emerald . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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IEEE Style Citation: Christopher Kezia Parimalam, J.D. Emerald, “Two – Dimensional Grammars Based on Patterns,” International Journal of Computer Sciences and Engineering, Vol.07, Issue.05, pp.216-220, 2019.

MLA Style Citation: Christopher Kezia Parimalam, J.D. Emerald "Two – Dimensional Grammars Based on Patterns." International Journal of Computer Sciences and Engineering 07.05 (2019): 216-220.

APA Style Citation: Christopher Kezia Parimalam, J.D. Emerald, (2019). Two – Dimensional Grammars Based on Patterns. International Journal of Computer Sciences and Engineering, 07(05), 216-220.

BibTex Style Citation:
@article{Parimalam_2019,
author = {Christopher Kezia Parimalam, J.D. Emerald},
title = {Two – Dimensional Grammars Based on Patterns},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {3 2019},
volume = {07},
Issue = {05},
month = {3},
year = {2019},
issn = {2347-2693},
pages = {216-220},
url = {https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=836},
doi = {https://doi.org/10.26438/ijcse/v7i5.216220}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v7i5.216220}
UR - https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=836
TI - Two – Dimensional Grammars Based on Patterns
T2 - International Journal of Computer Sciences and Engineering
AU - Christopher Kezia Parimalam, J.D. Emerald
PY - 2019
DA - 2019/03/10
PB - IJCSE, Indore, INDIA
SP - 216-220
IS - 05
VL - 07
SN - 2347-2693
ER -

           

Abstract

A language generating model called Pattern languages was introduced by Dassow , motivated by Angulin’s Pattern languages that use strings as language descriptors. Investigation of patterns has been of relevance in many areas such as combinatorics on words, learning theory and so on. Pattern grammars provide an alternative method in defining languages in automaton theory. Several methods to generate two-dimensional languages known as array languages or picture languages have been defined and investigated in literature and they have been extending the techniques and results of formal string language theory. A picture is defined as a rectangular array of terminal symbols in a rectangular plane. In this paper we extend the Pattern languages defined for strings by Dassow, to a two-dimensional case, while the simplicity and compactness of their descriptors as defined in one dimensional case are preserved. Hence, Two-dimensional Pattern languages are defined and investigated for their closure properties based on array operations.

Key-Words / Index Term

Two-dimensional patterns, Component, Two-dimensional axioms, Catenation, Factorization of arrays

References

[1] D. Angulin, “Finding Pattern common to set of strings,” Journal of Computer and System Sciences 21, 46-62, (1980)
[2] D. Giammarresi, A. Restivo, “Recognizable picture languages," International Journal of Pattern Recognition and Artificial Intelligence. 6:31-46, 1992.
[3] H. Fernau, Markus L. Schmid, K.G. Subramanian, “Two-Dimensional Pattern Languages”, In S.Bensch, F. Drewes, R. Freund, and F.Otto, editors, “Fifth Workshop on Non-Classical Models for Automata and Applications, NCMA, Volume 294 of books@ocg.at, pp.117-132. Osterreichische Computer Gesellschaft, 2013.
[4] J. Dassow, G.Paun, A.Salomaa, “Grammars based on Patterns,” International Journal of Foundations of Computer Science, Vol 4: 1-14, 1993.