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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.

12 votes
1 answer
418 views

Measuring the randomness of CNF formulas

Hence it seems that the randomness of a formula is not just a yes/no fact. … Questions Did anyone ever proposed a way to measure the randomness of a CNF formula? …
Giorgio Camerani's user avatar
9 votes
2 answers
622 views

Suppose $\mathbf{P} = \mathbf{BQP}$. Then what is randomness? Would it even exist at all?

But... what would randomness be then? Would it even exist at all? Would you be willing to continue to call it randomness? … Rather, the question boils down to the following: In a world where $\mathbf{P} = \mathbf{BQP}$, would randomness exist at all? …
Giorgio Camerani's user avatar
0 votes
1 answer
243 views

Upper bound on Independence Number of Random Regular Graph with degree $\Theta(\sqrt{|V|} \l...

Let $G=(V,E)$ be a random $\Delta$-regular graph with $\Delta \in \Theta(\sqrt{|V|} \log^2 |V|)$. I'm analysing an algorithm having asymptotic running time crucially depending on the Independence Numb …
Giorgio Camerani's user avatar