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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.
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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? …
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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? …
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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 …