Toward Solving Equations in Kleene Algebras

Authors:
F. Lajeunesse-Robert;B. Ktari
Affiliations:
Computer Science Department, Laval University, Quebec, Canada. E-mail: {francois.lajeunesse-robert, ktari}@ift.ulaval.ca;Computer Science Department, Laval University, Quebec, Canada. E-mail: {francois.lajeunesse-robert, ktari}@ift.ulaval.ca
Venue:
Proceedings of the 2007 conference on New Trends in Software Methodologies, Tools and Techniques: Proceedings of the sixth SoMeT_07
Year:
2007

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Abstract

This work aims to investigate conditions under which program analysis can be viewed as algebraically solving equations involving terms of subclasses of Kleene algebras and variables. In this paper, we show how to solve a kind of linear equations in which the variables appear only on one side of the equality sign, over an idempotent semiring with identity and zero. Furthermore, we give some ideas showing how to extend the resolution method to other classes of equations and algebraic structures.