### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 173-184 |

Number of pages | 12 |

Volume | 6224 LNCS |

DOIs | |

Publication status | Published - 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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 6224 LNCS, 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

**On müller context-free grammars.** / Ésik, Z.; Iván, Szabolcs.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 6224 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6224 LNCS, pp. 173-184, 14th International Conference on Developments in Language Theory, DLT 2010, London, ON, Canada, 8/17/10. https://doi.org/10.1007/978-3-642-14455-4_17

}

TY - GEN

T1 - On müller context-free grammars

AU - Ésik, Z.

AU - Iván, Szabolcs

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78049313622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78049313622&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14455-4_17

DO - 10.1007/978-3-642-14455-4_17

M3 - Conference contribution

SN - 3642144543

SN - 9783642144547

VL - 6224 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 173

EP - 184

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -