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Solving Algebraic Equations Using Coalgebra

Published online by Cambridge University Press:  15 January 2004

Federico De Marchi ,
Neil Ghani  and
Christoph Lüth
Federico De Marchi
Affiliation:
Mathematics and Computer Science, University of Leicester; fdm2@mcs.le.ac.uk., ng13@mcs.le.ac.uk.
Neil Ghani
Affiliation:
Mathematics and Computer Science, University of Leicester; fdm2@mcs.le.ac.uk., ng13@mcs.le.ac.uk.
Christoph Lüth
Affiliation:
FB 3 – Mathematics and Computer Science, Universität Bremen; cxl@tzi.de.
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Abstract

Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable categories rather than just Set; and ii) we define algebraic equations to allow right-hand sides which need not consist of finite terms. We show these generalized algebraic systems of equations have unique solutions by replacing the traditional metric-theoretic arguments with coalgebraic arguments.

Keywords

Coalgebrarecursioncategory theory.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 4: Fixed Points in Computer Science (FICS'02) , October 2003 , pp. 301 - 314
Copyright
© EDP Sciences, 2003

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