Is (a|b)* the same as a*|b*?

Is (a|b)* the same as a*|b*? In other words, does (a|b)* accept string which are combinations of as and bs?

Is (a|b)* the same as a*|b*?

They are not the same.

• a*|b* means "(0 or more as) or (0 or more bs)"

• (a|b)* means "0 or more (a or b)s"

So, for example, ab will be matched by (a|b)* but not by a*|b*. Note also that anything matched by a*|b* will also be matched by (a|b)*.