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What are pros and cons of using public version control system such as github for writing my papers and reports ?
Is it good to store copies of papers/reports being submitted to conference/journals on such repos. If no, wouldn't it make sense to not use them at the first place itself.
There are a few parts to your question, and I'm not sure which one is most important. If the question is about the value of version control, then you should see the answers to this question (which also has a link to a question about which one to use).
If you're asking about putting it on a shared repository, then here are some reasons:
If you're asking about making it public, so anyone can read/edit the paper, then I don't see much of an advantage in that. When the paper is done, it might be handy to be able to download the source of course.
One advantage of using those repositories (in public or private mode) is that you can show the changes and versions of some text. At the same time you can show variations of something through forks. Of course I have no idea why these features might be needed for publication of a paper, but if you are developing a paper collaboratively and you use some text based system, such as Latex, then it makes sense to use those repositories both for source sharing, backup and versioning, and alternative developments through forks. If you want to invite unidentified future authors (probably through fork) then it should be in public, otherwise private versions makes more sense for me.
