Is there a regular expression to detect a valid regular expression?

Question

Is it possible to detect a valid regular expression with another regular expression? If so please give example code below.

Answer 1

No, if you use standard regular expressions.

The reason is that you cannot satisfy the pumping lemma for regular languages. The pumping lemma states that a string belonging to language "L" is regular if there exists a number "N" such that, after dividing the string into three substrings x, y, z, such that |x|>=1 && |xy|<=N, you can repeat y as many times as you want and the entire string will still belong to L.

A consequence of the pumping lemma is that you cannot have regular strings in the form a^Nb^Mc^N, that is, two substrings having the same length separated by another string. In any way you split such strings in x, y and z, you cannot "pump" y without obtaining a string with a different number of "a" and "c", thus leaving the original language. That's the case, for example, with parentheses in regular expressions.