In this paper, we present a systematic way of deriving (1) languages of(generalised) regular expressions, and (2) sound and complete axiomatizationsthereof, for a wide variety of systems. This generalizes both the results ofKleene (on regular languages and deterministic finite automata) and Milner (onregular behaviours and finite labelled transition systems), and includes manyother systems such as Mealy and Moore machines.
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