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If you have a Kleene star applying to a set of characters not in any closure, does it apply to that whole string, or just the one character it belongs to? Any examples I search don't specify.

For example:

(A)BB*

Does this mean 1: one A followed by zero to an infinite number of BB's, or does it mean 2: one A followed by at least one B and zero to infinite number of B's?

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2 Answers 2

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Kleene stars applies to the character(s) it belongs, so in your example the correct option is the 2° one.

ABB* = {AB, ABB, ABBB, ABBBB, ..}

A(BB)* = {A, ABB, ABBBB, ABBBBBB, ..}

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  • $\begingroup$ Thank you, any explanations of the Kleene star always had it around brackets, which was clear but never when they were outside. $\endgroup$
    – NateH06
    Jan 22, 2017 at 11:14
  • $\begingroup$ "Kleene stars applies to the character(s) it belongs" Just using the word "belong" instead of "apply" doesn't actually convey any information. Which characters does it "belong" to? $\endgroup$
    – David Richerby
    Jan 22, 2017 at 11:35
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Conventionally, the Kleene star applies only to the character immediately before it, so $ABB^*$ is $AB$ followed by some number of $B$s. Parentheses are used to make it apply to a sequence of characters; e.g., $A(BB)^*$ is $A$ followed by some number of pairs of $B$s.

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