A Two-Dimensional Extension of Insertion Systems

Insertion systems are extended to two-dimensional models that are used to generate picture languages. Insertion rules are defined in terms of rows and columns. Using picture-insertion rules, we herein introduce two types of derivations that depend on the position at which the rules are applied. We obtain the relationships between the classes of languages generated by picture-insertion systems for each type of derivation and a number of two-dimensional computing models, such as tiling systems. Furthermore, we introduce regular control for the derivations in picture-insertion systems. Finally, we compare the classes of languages generated by picture-insertion systems with and without regular control.