More on Kleene Algebra

Abstract

In this lecture we will see how Kleene algebra can be used in a variety of situations involving *-like operations. The key result that allows these applications is that the n x n matrices over a Kleene algebra again form a Kleene algebra. Along the way we will establish a central lemma that establishes the importance of the regular sets Reg Σ over the finite alphabet Σ in reasoning about Kleene algebras in general.