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Electronic Colloquium on Computational Complexity

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Reports tagged with coin problem:
TR17-090 | 15th May 2017
Chin Ho Lee, Emanuele Viola

The coin problem for product tests

Let $X_{m, \eps}$ be the distribution over $m$ bits $(X_1, \ldots, X_m)$
where the $X_i$ are independent and each $X_i$ equals $1$ with
probability $(1+\eps)/2$ and $0$ with probability $(1-\eps)/2$. We
consider the smallest value $\eps^*$ of $\eps$ such that the distributions
$X_{m,\eps}$ and $X_{m,0}$ can be distinguished with constant
more >>>

TR18-157 | 10th September 2018
Nutan Limaye, Karteek Sreenivasiah, Srikanth Srinivasan, Utkarsh Tripathi, S Venkitesh

The Coin Problem in Constant Depth: Sample Complexity and Parity gates

Revisions: 2

The $\delta$-Coin Problem is the computational problem of distinguishing between coins that are heads with probability $(1+\delta)/2$ or $(1-\delta)/2,$ where $\delta$ is a parameter that is going to $0$. We study the complexity of this problem in the model of constant-depth Boolean circuits and prove the following results.

1. Upper ... more >>>

TR19-018 | 18th February 2019
Alexander Golovnev, Rahul Ilango, Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova, Avishay Tal

AC0[p] Lower Bounds against MCSP via the Coin Problem

Minimum Circuit Size Problem (MCSP) asks to decide if a given truth table of an $n$-variate boolean function has circuit complexity less than a given parameter $s$. We prove that MCSP is hard for constant-depth circuits with mod $p$ gates, for any prime $p\geq 2$ (the circuit class $AC^0[p])$. Namely, ... more >>>

TR19-087 | 10th June 2019
Rohit Agrawal

Coin Theorems and the Fourier Expansion

In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and the norms of the different levels of the Fourier expansion of functions in $\mathcal ... more >>>

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