Two – Dimensional Grammars Based on Patterns - Kezia Parimalam, Christopher; Emerald, j.D. Emerald (International Journal of Computer Sciences and Engineering, 2025)
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.