Comparing several lists based on multiple requirements

I am working on analyzing some data. The data is basically broken up into three pieces - machine names, installed applications, and a filtered application list. The filtered application list is a fairly short list of apps that I am interested in. The machine names list is a list of machines I am looking at. The installed application data piece is very long and shows each machine and all the applications installed on them. They installed applications tab looks like this.

Please Login or Register  to view this content.

The other tabs (machine names and filtered app list) are simply lists, something like this.

Please Login or Register  to view this content.

Please Login or Register  to view this content.

My goal is to write a formula that will sit next to each computer in the Machine Name tab and do some calculations. I want it to look through the list of Installed Applications that are associated with that particular machine name (from the Installed Applications tab), then check them against the Filtered Software List. If there are any matches, then it should say "Match" or "1" or something that I can count against. I've been trying to throw various array formulas at this but have had no success. My end goal is to determine which computers have ANY of the Filtered Software on them.