Line‐oriented two‐dimensional parallel computer languages

Line‐oriented two‐dimensional grammars (LOTDGs), region‐oriented two‐dimensional grammars (ROTDGs) and parallel productions are introduced. The relationships between LOTDGs and ROTDGs are stated. Examples of LOTDGS for generating all possible 45° right‐angled triangles, all possible squares, all possible 45° isosceles trapezoids, and all possible 45° parallelograms using parallel productions are presented. A new concise representation of a derivation chain is also introduced and illustrated by examples. LOTDGs and ROTDGs are compared. Generally speaking, LOTDGs require less terminal variables and non‐terminal variables, require less storage space, and require less derivation steps. Seven challenging problems for future research are also included. In addition, parallel production is an effective tool to model parallel computers as well as parallel processing. The results have useful applications in robot vision interpretation, robot pictorial communication, artificial intelligence, visual languages, software engineering, medical expert systems, and fuzzy logic functions.