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by brchr 3202 days ago
One of the key results on the role of randomness in polynomial identity testing is what's called the Schwartz–Zippel lemma.[1]

As the wiki article states, "Currently, there is no known sub-exponential time algorithm that can solve this problem deterministically. However, there are randomized polynomial algorithms for testing polynomial identities."

[1]https://en.wikipedia.org/wiki/Schwartz–Zippel_lemma

(Note that this is in the context specifically of polynomial function equivalence.)