This is what I would do:

• Create a HOH, with the first level keys being your computer names, and the second level keys being the patches installed on each computer.
• Assign the list of required patches to an array.
• Then iterate through the array using a for loop, and within that check whether the current element exists as a secondary key within your hash for each computer.

I hope that makes sense. Here is some code to demonstrate:

#!/usr/bin/perl -w
use strict;

my %computers;
my $computer;

my @required_patches = qw(
        KB893756
        KB893803
        KB896422
        KB896423
        KB899588
        KB899591
        KB911927
        KB921883
        );

while (my $line = <DATA>) {
    chomp($line);
    if ($line =~ /^KB\d{6}/) {
        $computers{$computer}{$line}++;
    }
    else {
        $computer = $line;
    }
}

for my $patch (@required_patches) {
    for my $computer (keys %computers) {
        if (!exists $computers{$computer}{$patch}) {
            print "$computer is missing patch $patch\n";
        }
    }
}

__DATA__
Computer1
KB893756
KB896422
KB896423
KB899588
KB899591
KB921883
Computer2
KB893756
KB896422
KB896423
KB899591
KB917159
KB921883
Computer3
KB893756
KB896422
KB899588
KB899591
KB917159
KB921883
[download]

Which prints:

Computer3 is missing patch KB893803
Computer2 is missing patch KB893803
Computer1 is missing patch KB893803
Computer3 is missing patch KB896423
Computer2 is missing patch KB899588
Computer3 is missing patch KB911927
Computer2 is missing patch KB911927
Computer1 is missing patch KB911927
[download]

Cheers,
Darren :)