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Results tagged with randomness
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user 40
Randomness is a key component of probabilistic algorithms, many combinatorial aarguments, the analysis of hashing functions, and in cryptography, among other applications.
12
votes
What is the most efficient way to generate a random permutation from probabilistic pairwise ...
Here's a somewhat interesting solution for $n=4$. The same idea also works for $n=6$.
Start with the switches $(0,1),(2,3)$ with probability $1/2$. Reducing $0,1$ to $X$ and $2,3$ to $Y$, we are in t …
- 14.5k
6
votes
Accepted
What is full-entropy bit-strings?
The meaning is a bit string $x$ which is distributed uniformly on $\{0,1\}^{|x|}$.
- 14.5k
15
votes
Accepted
Connectivity of a random regular graph of degree $d$
For constant $d \geq 3$, a random $d$-regular graph is connected with high probability. In fact, it is an expander with high probability. See for example this note by David Ellis. Friedman even showed …
- 14.5k
7
votes
Accepted
Where does the "intuitive" understanding of Kolmogorov complexity fails
The issue in play here is whether you use a self-terminating encoding (like your C example) or not. If you use a self-terminating encoding, then the subadditivity property does hold. If you don't (as …
- 14.5k