Abstract
The complexity of several decision problems concerning two-dimensional isometric array grammars (IAG) is studied. Because of the two-dimensional and the “isometric” properties of IAG, many decision problems become very hard to solve even for regular array grammars (RAG), the lowest subclass of IAG in the Chomsky-like hierarchy. In this paper, it is shown that the membership problems for RAGs and for context-free array grammars (CFAG) are both NP-complete. The emptiness problem and the equivalence problem for RAGs are shown to be undecidable.
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