### 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.

Original language | English |
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Title of host publication | Developments in Language Theory - 14th International Conference, DLT 2010, Proceedings |

Pages | 173-184 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Nov 4 2010 |

Event | 14th International Conference on Developments in Language Theory, DLT 2010 - London, ON, Canada Duration: Aug 17 2010 → Aug 20 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6224 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 14th International Conference on Developments in Language Theory, DLT 2010 |
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Country | Canada |

City | London, ON |

Period | 8/17/10 → 8/20/10 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Developments in Language Theory - 14th International Conference, DLT 2010, Proceedings*(pp. 173-184). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6224 LNCS). https://doi.org/10.1007/978-3-642-14455-4_17