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On Müller Context-Free Grammars

  • Zoltán Ésik
  • Szabolcs Iván
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6224)

Abstract

We define context-free grammars with Müller acceptance condition that generate languages of countable words. We establish several elementary properties of the class of Müller context-free languages including closure properties and others. We show that every Müller context-free grammar can be transformed into a normal form grammar in polynomial space without increasing the size of the grammar, and then we show that many decision problems can be solved in polynomial time for Müller context-free grammars in normal form. These problems include deciding whether the language generated by a normal form grammar contains only well-ordered, scattered, or dense words. In a further result we establish a limitedness property of Müller context-free grammars: If the language generated by a grammar contains only scattered words, then either there is an integer n such that each word of the language has Hausdorff rank at most n, or the language contains scattered words of arbitrarily large Hausdorff rank. We also show that it is decidable which of the two cases applies.

Keywords

Normal Form Polynomial Time Linear Order Order Type Countable Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Zoltán Ésik
    • 1
  • Szabolcs Iván
    • 1
  1. 1.Department of Computer ScienceUniversity of SzegedHungary

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