use strict;
use warnings;
no warnings qw /uninitialized/;

# \A anchor removed, so this is the same regex from the perlfaq.
my $re;
   $re = qr{
             \(
             (?:
                (?> [^()]+ )    # Non-parens without backtracking
              |
                (??{ $re })     # Group with matching parens
             )*
             \)
          }x;

while (<DATA>) {
    chomp;
    print "$_: ";

    # here is the proper place for the anchor
    print $& if /\A$re/;
    print "\n";
}

__DATA__
(*********)
(***(*)***)
((***))
(((***)))
((**)**(**))
(((())))