True, PDA's are the proper tool for balancing parenthesis. But it helps if it works... Your PDA would match "))((" perfectly find. Most wouldn't consider that balanced...

sub balanced
{
  my $string = shift;
  my $stack = 0;

  @string = split //, $string;
  for (@string) {
      last if $stack < 0;
      $stack++ if /[(]/;
      $stack-- if /[)]/;
  }
  return $stack ? 0 : 1;
}
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or, without using split and //:

sub balanced
{
  my $string = shift;
  my $stack = 0;

  for my $i (0..length($string)-1) {
    last if $stack < 0;
    $stack++ if substr($string,$i,1) eq '(';
    $stack-- if substr($string,$i,1) eq ')';
  }
  return $stack ?0 : 1;
}
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