n-dimensional array languages and description of crystal symmetry—I

Abstract

Following the general linguistic approach proposed by Narasimhan to pattern recognition we proposed two generative models,viz., the matrix models and the more powerful two-dimensional array models. In this paper we generalize the matrix models ton-dimensions and establish that then-dimensional matrix models are closed under union, concatenation, Kleene closure, ∈-free homomorphism, inverse homomorphism and intersection with regular matrices. Symmetry operations such as translation, reflection and half-turn are examined.