### Abstract

This paper shows that the collection of identities in two variables which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum does not have a finite equational axiomatization. This gives an alternative proof of the non-existence of a Finite basis for N—a result previously obtained by the authors.

Original language | English |
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Title of host publication | STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings |

Editors | Horst Reichel, Sophie Tison |

Publisher | Springer Verlag |

Pages | 267-278 |

Number of pages | 12 |

ISBN (Print) | 9783540671411 |

Publication status | Published - Jan 1 2000 |

Event | 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000 - Lille, France Duration: Feb 17 2000 → Feb 19 2000 |

### 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 | 1770 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000 |
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Country | France |

City | Lille |

Period | 2/17/00 → 2/19/00 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'On the two-variable fragment of the equational theory of the max-sum algebra of the natural numbers'. Together they form a unique fingerprint.

## Cite this

Aceto, L., Ésik, Z., & Ingólfsdóttir, A. (2000). On the two-variable fragment of the equational theory of the max-sum algebra of the natural numbers. In H. Reichel, & S. Tison (Eds.),

*STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings*(pp. 267-278). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1770). Springer Verlag.