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

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

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

  • $\begingroup$ * is reflexive, + is only transitive. $\endgroup$ – PleaseHelp Dec 2 '15 at 12:22
  • 2
    $\begingroup$ @calmyoursenses I would encourage everyone to use the notation that way but I can't guarantee that everybody actually does. $\endgroup$ – David Richerby Dec 2 '15 at 13:30

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