All reports by Author Shuichi Hirahara:

__
TR19-168
| 20th November 2019
__

Igor Carboni Oliveira, Lijie Chen, Shuichi Hirahara, Ján Pich, Ninad Rajgopal, Rahul Santhanam#### Beyond Natural Proofs: Hardness Magnification and Locality

__
TR19-025
| 28th February 2019
__

Shuichi Hirahara, Osamu Watanabe#### On Nonadaptive Reductions to the Set of Random Strings and Its Dense Subsets

__
TR18-138
| 10th August 2018
__

Shuichi Hirahara#### Non-black-box Worst-case to Average-case Reductions within NP

Revisions: 1

__
TR18-030
| 9th February 2018
__

Shuichi Hirahara, Igor Carboni Oliveira, Rahul Santhanam#### NP-hardness of Minimum Circuit Size Problem for OR-AND-MOD Circuits

__
TR17-092
| 10th May 2017
__

Shuichi Hirahara#### A Duality Between Depth-Three Formulas and Approximation by Depth-Two

__
TR17-073
| 28th April 2017
__

Eric Allender, Shuichi Hirahara#### New Insights on the (Non)-Hardness of Circuit Minimization and Related Problems

__
TR15-198
| 30th November 2015
__

Shuichi Hirahara, Osamu Watanabe#### Limits of Minimum Circuit Size Problem as Oracle

Revisions: 1

Igor Carboni Oliveira, Lijie Chen, Shuichi Hirahara, Ján Pich, Ninad Rajgopal, Rahul Santhanam

Hardness magnification reduces major complexity separations (such as $EXP \not\subseteq NC^1$) to proving lower bounds for some natural problem $Q$ against weak circuit models. Several recent works [OS18, MMW19, CT19, OPS19, CMMW19, Oli19, CJW19a] have established results of this form. In the most intriguing cases, the required lower bound is ... more >>>

Shuichi Hirahara, Osamu Watanabe

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 >>>

Shuichi Hirahara

There are significant obstacles to establishing an equivalence between the worst-case and average-case hardness of NP: Several results suggest that black-box worst-case to average-case reductions are not likely to be used for reducing any worst-case problem outside coNP to a distributional NP problem.

This paper overcomes the barrier. We ... more >>>

Shuichi Hirahara, Igor Carboni Oliveira, Rahul Santhanam

The Minimum Circuit Size Problem (MCSP) asks for the size of the smallest boolean circuit that computes a given truth table. It is a prominent problem in NP that is believed to be hard, but for which no proof of NP-hardness has been found. A significant number of works have ... more >>>

Shuichi Hirahara

We establish an explicit link between depth-3 formulas and one-sided approximation by depth-2 formulas, which were previously studied independently. Specifically, we show that the minimum size of depth-3 formulas is (up to a factor of n) equal to the inverse of the maximum, over all depth-2 formulas, of one-sided-error correlation ... more >>>

Eric Allender, Shuichi Hirahara

The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deals with time-bounded Kolmogorov complexity are prominent candidates for NP-intermediate status. We show that, under very modest cryptographic assumptions (such as the existence of one-way functions), the problem of approximating the minimum circuit size (or time-bounded Kolmogorov complexity) ... more >>>

Shuichi Hirahara, Osamu Watanabe

The Minimum Circuit Size Problem (MCSP) is known to be hard for statistical zero knowledge via a BPP-reduction (Allender and Das, 2014), whereas establishing NP-hardness of MCSP via a polynomial-time many-one reduction is difficult (Murray and Williams, 2015) in the sense that it implies ZPP $\neq$ EXP, which is a ... more >>>