Solving Linear Equations in *-continuous Action Lattices

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 variables appear only on one side of the equality sign, over a *-continuous action lattice. Furthermore, based on the method developed for solving equations, we present how model checking of a restricted version of the linear μ-calculus over finite traces can be done by algebraic manipulations. Finally, we give some ideas on how to extend the resolution method to other classes of equations and algebraic structures.