Non-Deterministic Kleene Coalgebras
Alexandra Silva, Marcello Bonsangue, Jan Rutten · Logical Methods in Computer Science · 2010
In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Milner (on regular behaviours and finite labelled transition systems), and includes many other systems such as Mealy and Moore machines.