# Significance of including $S \to ε$ production rule in regular grammar?

Why a production rule $S\to ε$ has been included in the definition of regular grammar? In that case, why it is restricted for $S$ (start symbol) to be present on right hand side of any production rule?

• It corresponds to the start state of a DFA or NFA being an accepting state: the empty string $\varepsilon$ is a member of the language. – BrianO Nov 14 '15 at 21:43

• This grammar shows that it's better not to allow $S$ on the right side at all. – Yuval Filmus Nov 14 '15 at 20:37
• I'd hardly call it a hack. How else would you efficiently define a regular grammar for $(aa)^*$? – Rick Decker Nov 15 '15 at 21:50