Kernel Level Event Detection

Kernel Level Event Detection

Is it possible to detect an event occurring in an application on Kernel
level?
For example, I have a very simple program that takes two input numbers,
adds them and displays the result. I wish to build another program which
detects when the addition in the first program is complete - This is an
event detection in some sense. (it does not wish the result, just needs to
know when the additon is done).
Now I do not wish to modify my first application to "send" some kind of
response when it is done adding. Is there some way I can contact the
kernel to notify me, when this particular application performs an
"addition", and I use this as proof that the addition has occured ?
(This may not be the best example, but I hope you get the idea. Another
example could be that I wish to detect when a browser (Chrome for e.g.)
has finished downloading a file, so I can sync it to my dropbox. Assume
that chrome fires no event on download complete and that I want to do it
without modifying the Chrome source code.)
Also, I wish to do it on Kernel Level because I wish the event detection
to be language independent. However, if there is any such feature in any
particular language, I would be interested in knowing it as well.
Any response would be appreciated. Thanks.