How to monitor a process running in Linux virtual machine from host windows machine?

I have installed a linux machine inside my Windows (using hyper-v server for that). Any idea how I could develop an application in c# which monitors a process running inside Linux machine. So for开发者_运维知识库 example it would monitor a process called "XYZ" inside linux and if that process was to go down and not exist it could simply display a red light in windows ?

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Run a small monitoring program inside linux which changes a flag in a database running on windows.

or change a file located in linux, which should be read from windows using some kind of file sharing ..

or run a small web server on linux to communicate from your program running on windows