A Note on Unambiguity, Finite Ambiguity and Complementation in Recognizable Two-Dimensional Languages

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The paper deals with some open questions related to unambiguity, finite ambiguity and complementation of two-dimensional recognizable languages. We give partial answers based on the introduction of special classes of languages of “high complexity”, in a sense specified in the paper and motivated by some necessary conditions holding for recognizable and unambiguous languages. In the last part of the paper we also show a new necessary condition for recognizable two-dimensional languages on unary alphabet.