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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.
9
votes
Accepted
When does randomization stops helping within PSPACE
There is a difficulty with the premise of your question — "when does randomization stops helping within $\mathrm{PSPACE}$ — because it suggests that the computational classes $\mathrm{X}$ such that $\ …
4
votes
What is the fastest known simulation of BPP using Las Vegas algorithms?
Barring any advances in derandomization, it seems to me as though the requirement that the Las Vegas Machine makes no mistakes is crucial, so that there is little to no benefit to having randomness at …
12
votes
Bounded depth probability distributions
Short answer.
For quantum circuits, there is at least one non-limitation result: arbitrary bounded-depth quantum circuits are unlikely to be simulatable with small multiplicative error in the probabi …