The Generative Power of d-Dimensional #-Context-Free Array Grammars

The main result proved in this paper shows that the natural embedding of any one-dimensional array language in the two-dimensional space can be generated by a two-dimensional #-context-free array grammar. This result can also be extended to the two-dimensional case, and we conjecture that a similar result is true for arbitrary dimensions. Our result shows that in the array case, context-freeness of a certain kind already yields universality. Furthermore, we exhibit the essence of undecidability lying in the proof of our main result, thereby extending some complexity results of Morita, Yamamoto, and Sugata 11] in passing.