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Results tagged with randomness
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user 129
Randomness is a key component of probabilistic algorithms, many combinatorial aarguments, the analysis of hashing functions, and in cryptography, among other applications.
22
votes
Problem in BPP but not known to be in RP or co-RP
An arguably more natural problem - not designed specifically for the purpose of finding a problem that might be in $\mathsf{BPP} \backslash \mathsf{RP} \cup \mathsf{coRP}$, and also not so closely rel …
- 38.5k
4
votes
Accepted
What is the probability that a random Boolean function has a trivial automorphism group?
Yes. To your first question, the probability goes to zero double-exponentially fast. This can be calculated as follows. For each permutation $\pi$, we can bound the probability that $\pi \in Aut(f)$, …
- 38.5k
9
votes
Accepted
Proof Strategies on P versus BPP
Although there aren't any problems known to be $\mathsf{BPP}$-complete (and Sipser gave an oracle relative to which $\mathsf{BPP}$ doesn't have complete problems), one topic to look at here is pseudor …
- 38.5k
5
votes
Accepted
Arithmetic Analogues of P versus BPP
There are several notions of randomness in computability theory (/the arithmetic hierarchy; lookup "Martin-Lof randomness", "Kurtz random", "Schnorr random", ...), but I think the ones that are analogous … The reason is essentially that a randomized Turing machine with bounded error can be simulated by a deterministic one: the deterministic one simulates the random one with all settings of the randomness …
- 38.5k