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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > SAMPLER:
Reports tagged with Sampler:
TR05-107 | 28th September 2005
Avi Wigderson, David Xiao

A Randomness-Efficient Sampler for Matrix-valued Functions and Applications

Revisions: 1

In this paper we give a randomness-efficient sampler for matrix-valued functions. Specifically, we show that a random walk on an expander approximates the recent Chernoff-like bound for matrix-valued functions of Ahlswede and Winter, in a manner which depends optimally on the spectral gap. The proof uses perturbation theory, and is ... more >>>


TR06-058 | 25th April 2006
Alexander Healy

Randomness-Efficient Sampling within NC^1

Revisions: 1

We construct a randomness-efficient averaging sampler that is computable by uniform constant-depth circuits with parity gates (i.e., in AC^0[mod 2]). Our sampler matches the parameters achieved by random walks on constant-degree expander graphs, allowing us to apply a variety expander-based techniques within NC^1. For example, we obtain the following results:

... more >>>

TR09-143 | 22nd December 2009
Noam Livne

On the Construction of One-Way Functions from Average Case Hardness

In this paper we study the possibility of proving the existence of
one-way functions based on average case hardness. It is well-known
that if there exists a polynomial-time sampler that outputs
instance-solution pairs such that the distribution on the instances
is hard on average, then one-way functions exist. We study ... more >>>


TR13-120 | 4th September 2013
Zeyu Guo

Randomness-efficient Curve Samplers

Curve samplers are sampling algorithms that proceed by viewing the domain as a vector space over a finite field, and randomly picking a low-degree curve in it as the sample. Curve samplers exhibit a nice property besides the sampling property: the restriction of low-degree polynomials over the domain to the ... more >>>


TR17-116 | 5th July 2017
Michal Moshkovitz, Dana Moshkovitz

Mixing Implies Strong Lower Bounds for Space Bounded Learning

With any hypothesis class one can associate a bipartite graph whose vertices are the hypotheses H on one side and all possible labeled examples X on the other side, and an hypothesis is connected to all the labeled examples that are consistent with it. We call this graph the hypotheses ... more >>>


TR17-161 | 30th October 2017
Mark Braverman, Gil Cohen, Sumegha Garg

Hitting Sets with Near-Optimal Error for Read-Once Branching Programs

Nisan (Combinatorica'92) constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2{n} + \log{n} \cdot \log(1/\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\log{n}+\log(1/\varepsilon))$, or to construct improved hitting sets, as ... more >>>




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