Kleene star meaning in regular expressions

Question

$\sum^*$ means all possible strings defined over $\sum$

Does it have the same meaning in regular expressions?

Answer 1

In regular expressions, the Kleene star basically means "zero or more of the preceding item". (Wikipedia says that "R* denotes the smallest superset of set described by R that contains ε and is closed under string concatenation. This is the set of all strings that can be made by concatenating any finite number (including zero) of strings from set described by R.") So the regular expression "a*" means "zero or more 'a's", e.g. "", "a", "aa", "aaa" etc.

Note that mathematical regular expressions are not necessarily always identical with the "regular expressions" used in programming, e.g. in the programming language Perl, due to the latter adding functionality such as backreferences. For this reason, sometimes people use the phrase "regexp" to distinguish programming language regular expressions from regular expressions in the mathematical sense.

If you're interested in the implementation of regular expression engines, you might like this article and this related discussion.