# Meaning of $\stackrel{*}{\rightarrow}$ production rule?

I've seen the production rule $\stackrel{*}{\rightarrow}$ in some papers concerning regular languages.

What's the meaning of $\stackrel{*}{\rightarrow}$ production rule?

• This is in the context of grammars, right? – Raphael Dec 2 '15 at 12:14
• I've placed the * where it belongs. Look at the source to see how. – Rick Decker Dec 2 '15 at 14:40
• @RickDecker I've certainly seen it in the other place, too. – Raphael Dec 2 '15 at 15:00

It's either the transitive closure or reflexive-transitive closure of $\rightarrow$. That is, $A\rightarrow B$ means that you get from $A$ to $B$ in exactly one step; $A\rightarrow^*B$ means either you get to $B$ in one or more steps (transitive closure) or in zero or more steps (reflexive-transitive closure).