my $re;
  $re = qr{
          (?:
             0            # 0
             (??{$re})    # Balanced 1's and 0's
             1            # 1
           |
             1            # 1
             (??{$re})    # Balanced 1's and 0's
             0            # 0
          )*
         }x;
   /^$re\z/;