Software Deployment

So you want the CA to run if this application OR a different application is not installed?
If so, I would use the appsearch functionality to search for the other application. The result will then be stored in a property, which makes the condition simple:
"If NOT Installed OR NOT <propertyname>".
Just remember to put the CA after the AppSearch SA.

I'm not exactly sure how to use the appsearch function, would you mind giving me a brief explanation? [;)]

AppSearch is (for some reason I'm not quite sure of) not able to search for an application directly. However, you can search for files, folders or components.
Personally, I would probably use AppSearch to look for the component that the exe-file of the other application is part of.

This would lead to the following:

AppSearch table:
Property: the name of the public property (all caps) to set if the component is found, for example "OTHERAPP"
Signature_: an identifier for this search, for example "SearchForApp"

CompLocator table:
Signature_: same as in the AppSearch table
ComponentId: the GUID of the component you are looking for
Type: 1

Now, the property OTHERAPP will be true if the component is installed on the target machine.
Then, just make sure your Custom Action is placed after the AppSearch SA, with a condition of "NOT Installed OR NOT OTHERAPP".

Hope this helps.

The best way here will be to use appsearch to look for the "Raw" registry key in HKLM\Software\Microsoft\Windows\Uninstall\<packageid> with any of the string and value pair that the package has made .

In the condition, check that if the value is not blank(or check it with the value you have in the package)