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Classes of two-dimensional languages and recognizability conditions

Published online by Cambridge University Press:  28 February 2011

Marcella Anselmo  and
Maria Madonia
Marcella Anselmo
Affiliation:
Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84084 Fisciano (SA), Italy; [email protected]
Maria Madonia
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125 Catania, Italy; [email protected]
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Abstract

The paper deals with some classes of two-dimensional recognizable languages of “high complexity”, in a sense specified in the paper and motivated by some necessary conditions holding for recognizable and unambiguous languages. For such classes we can solve some open questions related to unambiguity, finite ambiguity and complementation. Then we reformulate a necessary condition for recognizability stated by Matz, introducing a new complexity function. We solve an open question proposed by Matz, showing that all the known necessary conditions for recognizability of a language and its complement are not sufficient. The proof relies on a family of languages defined by functions.

Keywords

Two-dimensional languagesunambiguitycomplement
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 4 , October 2010 , pp. 471 - 488
Copyright
© EDP Sciences, 2011

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References

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