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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 $\ …
Niel de Beaudrap's user avatar
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 …
Niel de Beaudrap's user avatar
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 …
Niel de Beaudrap's user avatar