Can Regex Match Nested Brackets Without Recursion or Balancing Groups?

Matching Nested Brackets Without Recursion or Balancing Groups

The Challenge:
Can regex expressions, such as those in Java's java.util.regex, match arbitrarily nested brackets without relying on recursion or balancing groups?

The Solution:
Yes, it is possible using forward references:

(?=\()(?:(?=.*?\((?!.*?)(.*\)(?!.*).*))(?=.*?\)(?!.*?)(.*)).)+?.*?(?=)[^(]*(?=$)

How It Works:
This expression consists of several lookaheads and forward references that work together to identify nested groups of parentheses:

• (?=() ensures that the next character is an opening parenthesis.
• (?:...) ?.*?(?=...): A non-capturing group that iterates through the string.
• (?=.*?((?!.*?1): Lookahead to find the next opening parenthesis that is not part of the already-matched group (captured in 1).
• (.*)(?!.*2).*): Captures the rest of the string and matches at least one additional closing parenthesis.
• (?=.*?)(?!.*?2): Lookahead to find the next closing parenthesis that is not part of the already-matched group (captured in 2).
• .*?(?=1): Matches up to and including the last opening parenthesis found.
• [^(]*(?=2$): Matches up until the last closing parenthesis found, ensuring there are no more opening parentheses between them.

Example:
The following string will match three nested groups:

(F(i(r(s)t))) ((S)(e)((c)(o))(n)d) (((((((Third)))))))

Matching Inner Groups:
To match inner groups, a capturing group can be added to the end of the expression:

(?=\()(?=((?:(?=.*?\((?!.*?)(.*\)(?!.*).*))(?=.*?\)(?!.*?)(.*)).)+?.*?(?=)[^(]*(?=$)))

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