Projects per year

## Abstract

We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We deﬁne an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative equational theory whose free algebras correspond to well known structures. In each case we have ﬁnitary and continuous versions. The four cases are: Hausdorﬀ metrics from quantitive semilattices; pWasserstein metrics (hence also the Kantorovich metric) from barycentric algebras and also from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.

Original language | English |
---|---|

Title of host publication | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science : LICS'16, New York, NY, USA, July 5-8, 2016 |

Number of pages | 10 |

Publisher | Association for Computing Machinery |

Publication date | 2016 |

Pages | 700-709 |

ISBN (Print) | 978-1-4503-4391-6 |

DOIs | |

Publication status | Published - 2016 |

Event | 31st IEEE Symposium on Logic in Computer Science - Columbia University, New York City, United States Duration: 5 Jul 2016 → 8 Jul 2016 Conference number: 31st http://lics.rwth-aachen.de/lics16/ |

### Conference

Conference | 31st IEEE Symposium on Logic in Computer Science |
---|---|

Number | 31st |

Location | Columbia University |

Country | United States |

City | New York City |

Period | 05/07/2016 → 08/07/2016 |

Internet address |

## Fingerprint Dive into the research topics of 'Quantitative Algebraic Reasoning'. Together they form a unique fingerprint.

## Projects

- 1 Finished