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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.
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
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
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 …
CommunityBot
- 1
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