Toward Solving Equations in Kleene Algebras

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.