### Abstract

We give inequational and equational axioms for semirings with a fixed-point operator and formally develop a fragment of the theory of context-free languages. In particular, we show that Greibach’s normal form theorem depends only on a few equational properties of least pre-fixed-points in semirings, and elimination of chain- and deletion rules depend on their inequational properties (and the idempotency of addition). It follows that these normal form theorems also hold in non-continuous semirings having enough fixed-points.

Original language | English |
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Title of host publication | Computer Science Logic - 16th International Workshop, CSL 2002, 11th Annual Conference of the EACSL 2002, Proceedings |

Editors | Julian Bradfield |

Publisher | Springer Verlag |

Pages | 135-150 |

Number of pages | 16 |

ISBN (Print) | 3540442405, 9783540442400 |

DOIs | |

Publication status | Published - 2002 |

Event | 16th International Workshop on Computer Science Logic, CSL 2002 and 11th Annual Conference of the European Association for Computer Science Logic, EACSL 2002 - Edinburgh, United Kingdom Duration: Sep 22 2002 → Sep 25 2002 |

### 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 | 2471 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th International Workshop on Computer Science Logic, CSL 2002 and 11th Annual Conference of the European Association for Computer Science Logic, EACSL 2002 |
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Country | United Kingdom |

City | Edinburgh |

Period | 9/22/02 → 9/25/02 |

### Keywords

- Algebraically complete semirings
- Context-free languages
- Conway algebra
- Equational theory
- Greibach normal form
- Kleene algebra
- Pre-fixedpoint induction

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Ésik, Z., & Leiß, H. (2002). Greibach normal form in algebraically complete semirings. In J. Bradfield (Ed.),

*Computer Science Logic - 16th International Workshop, CSL 2002, 11th Annual Conference of the EACSL 2002, Proceedings*(pp. 135-150). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2471). Springer Verlag. https://doi.org/10.1007/3-540-45793-3_10