Abstract
A word language L is called generalized definite iff the membership of a word w in L depends only on the suffix and the prefix of w of fixed length. In an analogous way we introduce generalized definite tree languages where (viewing trees bottom-up) the prefix of length k is replaced by the set of "frontier-trees" of height less or equal than k and the suffix by "the subtree of height k at the root". We characterize definite tree languages using minimal automata and show that for regular tree languages the property "generalized definite" is decidable. In the proof a reduction of the problem to path properties shows that the size of minimal automata enters here in the same way as known for the case of word languages. We also give an characterization of generalized definiteness in terms of regular expressions and a special first-order logic.
The author was supported by the Deutsche Forschungsgemeinschaft.
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© 1989 Springer-Verlag Berlin Heidelberg
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Heuter, U. (1989). Generalized definite tree languages. In: Kreczmar, A., Mirkowska, G. (eds) Mathematical Foundations of Computer Science 1989. MFCS 1989. Lecture Notes in Computer Science, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51486-4_74
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DOI: https://doi.org/10.1007/3-540-51486-4_74
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