### Abstract

The words of a context-free language, ordered by the lexicographic ordering, form a context-free linear ordering. It is well-known that the linear orderings associated with deterministic context-free languages have a decidable monadic second-order theory. In stark contrast, we give an example of a context-free language whose lexicographic ordering has an undecidable first-order theory.

Original language | English |
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Title of host publication | Theoretical Computer Science - 7th IFIP TC 1/WG 2.2 International Conference, TCS 2012, Proceedings |

Pages | 104-118 |

Number of pages | 15 |

DOIs | |

Publication status | Published - 2012 |

Event | 7th IFIP International Conference on Theoretical Computer Science, TCS 2012 - Amsterdam, Netherlands Duration: Sep 26 2012 → Sep 28 2012 |

### 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 | 7604 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 7th IFIP International Conference on Theoretical Computer Science, TCS 2012 |
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Country | Netherlands |

City | Amsterdam |

Period | 9/26/12 → 9/28/12 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Carayol, A., & Ésik, Z. (2012). A context-free linear ordering with an undecidable first-order theory. In

*Theoretical Computer Science - 7th IFIP TC 1/WG 2.2 International Conference, TCS 2012, Proceedings*(pp. 104-118). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7604 LNCS). https://doi.org/10.1007/978-3-642-33475-7_8