Abstract:

In this talk, I will be giving an overview of the main results of my PhD thesis. More concretely, I will show how the classical notion of regular expression, proposed by Kleene in 1956, can be generalized for a larger class of models of computation, in a uniform way, by using coalgebraic modeling. Interesting models covered by the framework include Mealy machines and probabilistic automata. We will also show how to axiomatize the languages of regular expressions proposed. This constitutes a generalization of Kozen's axiomatization of classical regular expressions.