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
Hlavní autoři: Mardare, Radu, Panangaden, Prakash, Plotkin, Gordon
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: New York, NY, USA ACM 05.07.2016
Edice:ACM Conferences
Témata:
Theory of computation
Theory of computation > Logic
Theory of computation > Models of computation
Theory of computation > Models of computation > Computability
ISBN:9781450343916, 1450343910
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Shrnutí: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.
ISBN:9781450343916
1450343910
DOI:10.1145/2933575.2934518