There are many approaches to finding out about the execution and/or completion [assumed complete if not running] of another process.

1) Have the other program write a file as it starts, and delete it upon its exit. Then, you just need to check if the file exists.
2) By checking for parameters with the 'grep' at the end of a
>ps -ef | grep ___
3) By checking for the existence of specific files [assuming you can run lsof - which may need to be installed]. lsof does a list of open files.
>lsof | grep ___