Proof that the language classes accepted by DFAs and NDFAs coincide. Algebraic operations on languages. Finite union and intersection, concatenation, and Kleene closure. Regular expressions and the languages they denote. Examples of regular languages, including recognisers.
Regular languages are representable events.
Arden's rule as a recursive definition. Its proof by induction. Extension to matrices of events. Statement of Kleene's Theorem, including an overview of the proof structure. Representable events have regular expressions.