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Wikipedia has a nice list of various proof-of-work functions: https://en.wikipedia.org/wiki/Proof-of-work_system#List_of_p...

As for "lottery", I believe the answer is yes and no. The basic point is to raise the cost of "faking" a confirmation, and how you do that is completely up to you - e.g. captchas are a great example! That said, the random part of the non-deterministic process provides a lot of really nice properties for a distributed system - fairness claims, etc. That said, this is a deep topic (with lots of caveats) in its own right.



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