Questions tagged [pseudorandom-generators]

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4
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0answers
138 views

More powerful generator than Nisan-Wigderson one

Nisan-Wigderson generator can be computed in $\log^{O(1)} n$ space and fools all constant-depth circuits of size poly($n$). I mean Theorem 5 here. I want another generator, that can be computed in ...
4
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0answers
91 views

Sampling Functions Efficiently vs Pseudorandom Generators

Let $X$ be a set of $n$-bit Boolean functions of the form $f:\{0,1\}^n\rightarrow \{0,1\}$. For instance, $X$ could be the set of $n$-bit monotone Boolean functions, or the set of $n$-bit functions ...
4
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0answers
100 views

Looking for an exposition of the proof of the LMN theorem

Is there any lecture note or review paper which gives a self-contained proof of the Linial-Mansour-Nisan theorem? The exposition of that in Ryan O'Donnel's book seems to use terminology and notation ...
4
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0answers
78 views

Inefficient pseudorandom distribution using a few random bits

In these slides, it is mentioned that for a class of functions $\mathcal{C}$, a pseudorandom generator is a distribution $D$ such that $D$ fools $\mathcal{C}$. $D$ is efficiently samplable. $D$ is ...
3
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0answers
175 views

Why are one way functions and pseudorandom number generators considered necessary or essential for derandomization?

If strong pseudorandom number generator exists then $BPP=P$ holds and if one way functions exists then $BPP\subseteq SUBEXP$ holds. What are the best statements we have proved that come close to ...
2
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0answers
114 views

What upper bound can we get under 3-wise independence? (comparable edition)

Here is the original question: What bound can we get using $k$-th moment inequality under 3-wise independence? .Yury has given a 3-wise independent example that shows the upper bound is no better than ...
1
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0answers
243 views

On $BPP$ in $P^{NP}$ and $SETH$

It is believed showing $BPP$ in $P$ involves good $PRG$s and faces lower bound barriers. Does showing $BPP$ in $P^{NP}$ which would mean $BPP\neq EXP^{NP}$ face similar $PRG$ and give lower bounds? ...
1
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0answers
142 views

How does one sample uniformly at random from an uncountably infinite set?

I want to know if there are any examples of polynomial time algorithms which can sample uniformly at random from a given uncountably infinite set? (assuming it is possible) Does it help if the sample ...
1
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0answers
103 views

Extractor with somewhat corrupted seeds

In conditional min-entropy extractor, there is a joint distribution $(X,Y)$ such that if the average min-entropy (for some appropriate notion of it) ${\rm H}_\infty(X|Y)$ is large, then ${\rm Ext}(X, ...
1
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0answers
164 views

A question about combinatorial design in Nisan-Wigderson Generator

Let $[d]$ be a universe and $S_1, \dots, S_m$ be an $(\ell, a)$-design over $[d]$ which means that: $\forall i \in [m], S_i \subseteq [d], |S_i|=\ell$. $\forall i \neq j \in [m]$, $|S_i \cap S_j| \...
1
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0answers
133 views

Structured Graph Generation

I hope you can help. I am looking for the best way to generate random bipartite graphs with localised structure within one of the node types. Such that type A visits a local group of type B with a ...