my $re;
  $re = qr{
          (?:
             0            # 0
             (??{$re})    # Balanced 1's and 0's
             1            # 1
           |
             1            # 1
             (?>          # If I get here, do not backtrack!
               (??{$re})  # Balanced 1's and 0's
             )
             0            # 0
          )*?
         }x;
   for (qw(1001 11100 000111 00111), "101"x50) {
     if (/^$re\z/) {
       print "$_ matched\n";
     }
     else {
       print "$_ did not match\n";
     }
   }