Regular Expression: Mathematically vs. Programmatically

Question

Consider the following regular expressions:

1. 7+
2. (7)+

Does anyone that is very familiar with regular expression theory in Mathematics agree that the two regular expressions are semantically the same?

Answer 1

Yes, those two regular expressions are the same because they both recognize the same language. The fact that they are not written identically is just a notational issue.

Answer 2

Programmatically (as in evaluated by the regular expression engine of a language) it only differs in the capturing groups resulting.

Other than that, they are the same. It is as writing ((7) + (1)) as opposed as 7 + 1. They evaluate to are the same. (Yeah, mathematically speaking, regular languages doesn't evaluate to anything)

Answer 3

Do they describe the same language? Yes. Do they mean the same thing to someone trying to interpret the language? No. The second one tells me that I should be more interested in the 7s.

Answer 4

The second reduces to first. Do you agree that

 ab+

and

 a(b)+

and

 (ab)+

are semantically different?

Answer 5

The only difference is the parens assign the enclosed pattern to a group so you can reference that little piece after it's been evaluated.