((A & B)' | (A & C & (A & B & D)')); 

##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;

my $x = '((A & B)\' | (A & C & (A & B & D)\'))'; 

print "Given: $x\n"; 

$x =~ s/(\(.*?\))\'/\!$1/g; 

print "Calculated: ",$x,"\n";


##</code><code>##

Given: ((A & B)' | (A & C & (A & B & D)')) 
Calculated: (!(A & B) | !(A & C & (A & B & D)))