Parallel Contextual Hexagonal Array Grammars and Languages

Authors:
D. G. Thomas;M. H. Begam;N. G. David
Affiliations:
Department of Mathematics, Madras Christian College, Tambaram, Chennai, India 600 059;Department of Mathematics, Madras Christian College, Tambaram, Chennai, India 600 059;Department of Mathematics, Madras Christian College, Tambaram, Chennai, India 600 059
Venue:
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Year:
2009

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Abstract

Hexagonal patterns are known to occur in the literature on picture processing and image analysis. Siromoney et al. constructed hexagonal array grammars for generating hexagonal arrays and hexagonal patterns. On the other hand, Marcus introduced a class of grammars called contextual grammars in contrast to Chomskian grammars that generate words by starting with an initial word and adding iteratively pairs of words called contexts associated to a set of words called selector to the words already obtained. In this paper, we develop a new method of generating hexagonal arrays based on an extension of contextual grammars called parallel contextual hexagonal array grammars. We present necessary conditions for classification of parallel contextual hexagonal array languages, compare with other hexagonal array generating models and study closure properties under union.