Assuming that Σ = {a, b}, I want to find out the regular expression (RE) Σ* (that being the set of all possible strings over the alphabet Σ).
I came up with below two possibilities:
(a+b)*
(a*b*)*
However, I can't decide by myself which RE is correct, or if both are bad. So, please tell me the correct answer.
The + operator is typically used to indicate union (|, "or") in academic regular expressions, not "one or more" as it typically means in non-academic settings (such as most regex implementations).
So, a+b means [ab] or a|b, thus (a+b)* means any string of length 0 or more, containing any number of as and bs in any order.
Likewise, (a*b*)* also means any string of length 0 or more, containing any number of as and bs in any order.
The two expressions are different ways of expressing the same language.