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REPORTS > KEYWORD > HITTING SET GENERATORS:
Reports tagged with Hitting set generators:
TR19-025 | 28th February 2019
Shuichi Hirahara, Osamu Watanabe

#### On Nonadaptive Reductions to the Set of Random Strings and Its Dense Subsets

Revisions: 1

We investigate the computational power of an arbitrary distinguisher for (not necessarily computable) hitting set generators as well as the set of Kolmogorov-random strings. This work contributes to (at least) two lines of research. One line of research is the study of the limits of black-box reductions to some distributional ... more >>>

TR19-065 | 1st May 2019
Mrinal Kumar, Ramprasad Saptharishi, Noam Solomon

#### Derandomization from Algebraic Hardness: Treading the Borders

Revisions: 3

A hitting-set generator (HSG) is a polynomial map $Gen:\mathbb{F}^k \to \mathbb{F}^n$ such that for all $n$-variate polynomials $Q$ of small enough circuit size and degree, if $Q$ is non-zero, then $Q\circ Gen$ is non-zero. In this paper, we give a new construction of such a HSG assuming that we have ... more >>>

TR20-103 | 9th July 2020
Mahdi Cheraghchi, Shuichi Hirahara, Dimitrios Myrisiotis, Yuichi Yoshida

#### One-Tape Turing Machine and Branching Program Lower Bounds for MCSP

Revisions: 1

For a size parameter $s\colon\mathbb{N}\to\mathbb{N}$, the Minimum Circuit Size Problem (denoted by ${\rm MCSP}[s(n)]$) is the problem of deciding whether the minimum circuit size of a given function $f \colon \{0,1\}^n \to \{0,1\}$ (represented by a string of length $N := 2^n$) is at most a threshold $s(n)$. A ... more >>>

TR20-143 | 16th September 2020
Shuichi Hirahara

#### Characterizing Average-Case Complexity of PH by Worst-Case Meta-Complexity

We exactly characterize the average-case complexity of the polynomial-time hierarchy (PH) by the worst-case (meta-)complexity of GapMINKT(PH), i.e., an approximation version of the problem of determining if a given string can be compressed to a short PH-oracle efficient program. Specifically, we establish the following equivalence:

DistPH is contained in ... more >>>

TR21-014 | 15th February 2021
Dori Medini, Amir Shpilka

#### Hitting Sets and Reconstruction for Dense Orbits in VP$_e$ and $\Sigma\Pi\Sigma$ Circuits

In this paper we study polynomials in VP$_e$ (polynomial-sized formulas) and in $\Sigma\Pi\Sigma$ (polynomial-size depth-$3$ circuits) whose orbits, under the action of the affine group GL$^{aff}_n({\mathbb F})$, are dense in their ambient class. We construct hitting sets and interpolating sets for these orbits as well as give reconstruction algorithms.

As ... more >>>

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