Quantitative Algebraic Reasoning
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...
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| Vydáno v: | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science s. 700 - 709 |
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| Jazyk: | angličtina |
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New York, NY, USA
ACM
05.07.2016
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| ISBN: | 9781450343916, 1450343910 |
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| 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; p-Wasserstein 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. |
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| AbstractList | 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; p-Wasserstein 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. |
| Author | Panangaden, Prakash Mardare, Radu Plotkin, Gordon |
| Author_xml | – sequence: 1 givenname: Radu surname: Mardare fullname: Mardare, Radu email: mardare@cs.aau.dk organization: Aalborg University, Denmark – sequence: 2 givenname: Prakash surname: Panangaden fullname: Panangaden, Prakash email: prakash@cs.mcgill.ca organization: McGill University, Canada – sequence: 3 givenname: Gordon surname: Plotkin fullname: Plotkin, Gordon email: gdp@inf.ed.ac.uk organization: University of Edinburgh, UK |
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| Snippet | We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed by rationals: a = ε b... |
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| SubjectTerms | Theory of computation Theory of computation -- Logic Theory of computation -- Models of computation Theory of computation -- Models of computation -- Computability |
| Title | Quantitative Algebraic Reasoning |
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