I want to break into academia by becoming a PhD student of computer science. However, I need publications and letters of recommendation in order to strengthen my application. The ordinary way of doing this, as I understand it, is to become a masters student and publish in the course of earning that degree.
That seems wasteful to me. I've taken graduate level courses. I can write a proof. I know my way around the pumping lemmas. I have read higher level papers and texts on my own.
Having an advisor or mentor would help, though. I don't know what's a reasonable problem to study, and publication has some arcane processes that an advisor might help me to understand.
How do I go about contacting a potential advisor? Is this even a reasonable course of action?