f-generated Kleene Algebra

Abstract:
When describing iterations or loops it is well known and common to use the Kleene star. We first show an example for iteration, where the star operation is not adequate, since it just iterate and do not modify the iterated element. Therefore we introduce, as a generalisation of Kleene algebra, the structure of f-generated Kleene algebra, that have an iteration operation which depends on a function f and modify the iterated element in each step.