Quantitative algebraic reasoning
Mardare, Radu and Panangaden, Prakash and Plotkin, Gordon; (2016) Quantitative algebraic reasoning. In: LICS '16 : Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, USA, pp. 700709. ISBN 9781450343916

Text (MardareetalLICS2016Quantitativealgebraicreasoning)
Mardare_etal_LICS2016_Quantitative_algebraic_reasoning.pdf Accepted Author Manuscript Download (328kB) Preview 
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.
Creators(s):  Mardare, Radu, Panangaden, Prakash and Plotkin, Gordon; 

Item type:  Book Section 
ID code:  70265 
Keywords:  algebraic reasoning, quantitative algebra, probabilistic programming, semantics, computer circuits, reconfigurable hardware, equality relations, equational theory, Kantorovich metric, Mathematics, Software, Mathematics(all) 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Computer and Information Sciences 
Depositing user:  Pure Administrator 
Date deposited:  24 Oct 2019 11:05 
Last modified:  20 Jan 2021 16:16 
URI:  https://strathprints.strath.ac.uk/id/eprint/70265 
Export data: 