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Randomness is a key component of probabilistic algorithms, many combinatorial aarguments, the analysis of hashing functions, and in cryptography, among other applications.

18 votes
2 answers
561 views

Natural theorems proven only "to high probability"?

There are plenty of situations where a randomized "proof" is much easier than a deterministic proof, the canonical example being polynomial identity testing. Question: Are there any natural mathema …
Geoffrey Irving's user avatar
10 votes
1 answer
271 views

Is deterministic pseudorandomness possibly stronger than randomness in parallel?

Let the class BPNC (the combination of $\mathsf{BPP}$ and $\mathsf{NC}$) be log depth parallel algorithms with bounded error probability and access to a random source (I'm not sure if this has a diffe …
Geoffrey Irving's user avatar