Equi-triangular array grammars with equal matrix type of rules

Abstract

Generation of two-dimensional languages of picture arrays, rectangular, triangular or hexagonal in shape, has been considered in several studies motivated by problems in picture processing and pattern recognition. Picture arrays in the form of equi-triangular arrays (et-arrays) composed of equilateral triangles and their generation by context-free type of array grammars have been considered recently. Here generation of picture languages of equi-triangular arrays based on equal matrix grammar type of rules is introduced and investigated. The rules in the matrix are regular type of rules except for initial rules. It has been proved that these equi-triangular array grammars with equal matrix grammar type of rules can generate picture languages of et-arrays that cannot be generated by context-free equi-triangular array grammars. Also the family of equi-triangular array grammars with equal matrix type of rules is shown to properly include the family of regular picture languages of et-arrays.