The relationship between parallel isometric array languages and sequential isometric array languages is examined. Their hierarchical structures are inves­tigated and a hierarchy is completed by introducing parallel context-free array languages (PCFAL), derivation bounded array languages (DBAL), linear array lang­uages (LAL) and extended regular array languages (ERAL). It is interesting to find that some fundamental aspects that hold in 1-dimensional; string languages do not hold in their 2-dimensional counterparts.

Some parsing techniques are also explored. It is shOIJn that while parallel, parsing grammars may be much simpler to write and parallel processing usually takes less time than sequential ones, the nature of parallel parsing is very complicated.

Finally, several future research topics concerning with parallel isometric array languages including their complexities, hierarchical structures and applica­tion to pattern recognition are discussed.