• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Computational Complexity of Minimum Description Size Problems

Research Project

Project/Area Number 18H04090
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Review Section Medium-sized Section 60:Information science, computer engineering, and related fields
Research InstitutionTokyo Institute of Technology

Principal Investigator

渡辺 治  東京工業大学, その他, 理事・副学長 (80158617)

Co-Investigator(Kenkyū-buntansha) 伊東 利哉  東京工業大学, 情報理工学院, 教授 (20184674)
天野 一幸  群馬大学, 大学院理工学府, 教授 (30282031)
玉置 卓  兵庫県立大学, 社会情報科学部, 准教授 (40432413)
森 立平  東京工業大学, 情報理工学院, 助教 (60732857)
平原 秀一  国立情報学研究所, 情報学プリンシプル研究系, 助教 (80848440)
清水 伸高  東京工業大学, 工学院, 助教 (10910127)
Project Period (FY) 2018-04-01 – 2022-03-31
Project Status Granted (Fiscal Year 2021)
Budget Amount *help
¥38,480,000 (Direct Cost: ¥29,600,000、Indirect Cost: ¥8,880,000)
Fiscal Year 2021: ¥10,530,000 (Direct Cost: ¥8,100,000、Indirect Cost: ¥2,430,000)
Fiscal Year 2020: ¥10,530,000 (Direct Cost: ¥8,100,000、Indirect Cost: ¥2,430,000)
Fiscal Year 2019: ¥10,660,000 (Direct Cost: ¥8,200,000、Indirect Cost: ¥2,460,000)
Fiscal Year 2018: ¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Keywords最小記述量 / 最小記述量計算 / P≠NP予想 / 計算論的学習理論 / 一方向関数 / 多項式時間階層 / 平均時計算困難性 / 計算論的暗号 / PAC学習困難性 / 最小記述量計算問題 / 機械学習 / P≠NP予想 / 平均時計算量 / 平均時計算複雑度 / 学習可能性 / 情報セキュリティ / 情報セキュリティ技術 / 最小回路サイズ問題 / 回路計算量 / 質問計算量 / SAT問題 / 量子計算の基礎
Outline of Annual Research Achievements

これまでの研究の中から最小記述量計算問題の計算困難さに関連する様々な結果が出始めてきたが,本年度は,それをさらに進めて,最小記述量計算問題をコルモゴロフ記述量ならびに機械学習可能性(正確にはPAC学習複雑度)と関連付け,それにより,NP問題全般(あるいはもう少し広い多項式時間階層,クラスPH)の平均時複雑度へ関連付ける研究を進めた。その中で得られた結果のうちで主要なものを以下に述べる。
1.多項式時間階層クラスPHの平均時計算複雑度を小記述長問題の最悪時計算複雑度により特徴づけることに成功した。その結果として,PHに対する困難性増幅定理を得た。たとえば,PHの代表的な問題に対して,その1%の入力が効率的に解けることとPHのすべての問題に対して,その99%の入力が効率的に解けることが同値であることがわかった。
2.PHの最悪時計算複雑度を平均時計算複雑度に結び付ける重要な手法の一つに,PHの最悪時計算困難性をもとに計算論的暗号素(computationally secure cryptographic primitive)を作り出す手法が考えられる。しかし,そのような手法は,通常の計算論的解析(より正確には,black-box的な並列乱択還元を用いた解析)では不可能であることを示した。その証明においては,PHの構造的困難さ(より正確には密でない集合への還元可能性)について,既存の特徴づけを大幅に改良する特徴づけを与える技法を開発した。
3.従来の学習の枠組みならびに暗号の枠組みを拡張することにより,(その枠組みの上での)PAC学習困難性と計算論的暗号素の構成可能性間の同値性を示すことができた。なお,これは本研究課題でRAとして雇用している博士課程学生の独自研究である。
4.3SAT問題に対して,指数関数時間ではあるが(その時点での)世界最速の乱択アルゴリズムを得た。

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

課題の主目標である最小記述量の計算複雑さに関連する学習困難性と計算論的暗号素の存在性をNPやPHなど、代表的な計算量クラスに対する平均時計算困難性に結び付ける手がかりを得ることができたため。また、博士課程学生を含め、若手研究者が活発に研究し、これらの成果を挙げていることについても大変期待が持てるため。

Strategy for Future Research Activity

機械学習(とくにPAC学習)は,最小記述量計算問題の変形の一つと見ることができる。本年度の成果により,そのPAC学習の困難さの計算論的な特徴づけをかなり明確にすることができた。来年度は,これをさらに進めて,より明確で,より直接的な特徴づけを得ることを目指す。それには、最小記述量の代表例であるコルモゴロフ複雑度の計算との関係が重要となると思われる。また,より具体的な対象を用いた問題の計算複雑さの研究,さらには具体的な計算困難問題からの一方向関数の構成について,より明確な関係の解明を目指す。以上により,本研究課題において目指した最小記述量の計算困難さを中心に,一方向関数や機械学習可能性のより深い意味での関連について,統一的な解釈にいくらかでも近づけるような結果を最終年度のとりまとめとして得ることを目指す。

Report

(3 results)
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report

Research Products

(56 results)

All 2021 2020 2019 2018 Other

All Int'l Joint Research (3 results) Journal Article (36 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 36 results,  Open Access: 6 results) Presentation (17 results) (of which Int'l Joint Research: 7 results,  Invited: 2 results)

  • [Int'l Joint Research] Humboldt-University at Berlin(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University of Rochester(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Oxford University(英国)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] On the Minimum Number of Pieces for Two-Dimensional Anti-Slide Using T-Tetrominoes2021

    • Author(s)
      KIMURA Kento、AMANO Kazuyuki、ARAKI Tetsuya
    • Journal Title

      IEICE Trans. Inf. & Syst.

      Volume: E104.D Issue: 3 Pages: 355-361

    • DOI

      10.1587/transinf.2020fcp0007

      10.1587/transinf.2020FCP0007

    • NAID

      130007993186

    • ISSN
      0916-8532, 1745-1361
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Simple and Fast Algorithm for Computing the <i>N</i>-th Term of a Linearly Recurrent Sequence2021

    • Author(s)
      Bostan Alin and Mori Ryuhei
    • Journal Title

      in Proc. SODA 2021

      Volume: SIAM Pages: 118-132

    • DOI

      10.1137/1.9781611976496.14

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On nonadaptive security reductions of hitting set generators2020

    • Author(s)
      Shuichi Hirahara and Osamu Watanabe
    • Journal Title

      in Proc. APPROX/RANDOM 2020

      Volume: LIPIcs 176(15)

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Unexpected hardness results for Kolmogorov complexity under uniform reductions2020

    • Author(s)
      Shuichi Hirahara
    • Journal Title

      in Proc. ACM STOC 2020

      Volume: ACM Pages: 1038-1051

    • DOI

      10.1145/3357713.3384251

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-disjoint promise problems from meta-computational view of pseudorandom generator constructions2020

    • Author(s)
      Shuichi Hirahara
    • Journal Title

      in Proc. CCC 2020

      Volume: LIPIcs 169

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterizing Average-Case Complexity of PH by Worst-Case Meta-Complexity2020

    • Author(s)
      Hirahara Shuichi
    • Journal Title

      in Proc. IEEE FOCS 2020

      Volume: IEEE Pages: 50-60

    • DOI

      10.1109/focs46700.2020.00014

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Competitive analysis for two variants of online metric matching problem2020

    • Author(s)
      Toshiya Itoh, Shuichi Miyazaki, and Makoto Satake
    • Journal Title

      in Proc. COCOA 2020

      Volume: LNCS 12577 Pages: 486498-486498

    • DOI

      10.1007/978-3-030-64843-5_33

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On basing auxiliary-input cryptography on NP-Hardness via nonadaptive black-box reductions2020

    • Author(s)
      Mikito Nanashima
    • Journal Title

      in Proc. ITCS 2020

      Volume: LIPIcs 185

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Extending learnability to auxiliary-input cryptographic primitives and meta-PAC learning2020

    • Author(s)
      Mikito Nanashima
    • Journal Title

      in Proc. COLT 2020

      Volume: PMLR 125 Pages: 2998-3029

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Additive-error fine-grained quantum supremacy2020

    • Author(s)
      Morimae Tomoyuki、Tamaki Suguru
    • Journal Title

      Quantum

      Volume: 4 Pages: 329-329

    • DOI

      10.22331/q-2020-09-24-329

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] An improvement of the algorithm of Hertli for the unique 3SAT problem2020

    • Author(s)
      Qin Tong、Watanabe Osamu
    • Journal Title

      Theoretical Computer Science

      Volume: 806 Pages: 70-80

    • DOI

      10.1016/j.tcs.2018.11.023

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Size of Depth-Two Threshold Circuit for Inner Product Mod 2 Function2020

    • Author(s)
      Kazuyuki Amano
    • Journal Title

      Proc. of 14th Int. Conf. on Language and Automata Theory and Applications

      Volume: 12038 Pages: 235-247

    • DOI

      10.1007/978-3-030-40608-0_16

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Approximation Algorithm for the 2-Dispersion Problem2020

    • Author(s)
      Kazuyuki Amano and Shin-ichi Nakano
    • Journal Title

      IEICE Trans. Inf. & Syst.

      Volume: E103-D-3 Issue: 3 Pages: 506-508

    • DOI

      10.1587/transinf.2019fcp0005

      10.1587/transinf.2019FCP0005

    • NAID

      130007804167

    • ISSN
      0916-8532, 1745-1361
    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Nonadaptive Reductions to the Set of Random Strings and Its Dense Subsets2020

    • Author(s)
      Hirahara Shuichi、Watanabe Osamu
    • Journal Title

      Complexity and Approximation - In Memory of Ker-I Ko

      Volume: LNCS 12000 Pages: 67-79

    • DOI

      10.1007/978-3-030-41672-0_6

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On XOR Lemmas for the Weight of Polynomial Threshold Functions2019

    • Author(s)
      Kazuyuki Amano and Shoma Tate
    • Journal Title

      Information and Computation

      Volume: 269 Pages: 104439-104439

    • DOI

      10.1016/j.ic.2019.104439

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Number of p4-tilings by an N-omino2019

    • Author(s)
      Kazuyuki Amano and Yoshinobu Haruyama
    • Journal Title

      International Journal of Computational Geometry & Applications

      Volume: 29-1 Pages: 3-19

    • DOI

      10.1142/s0218195919400016

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Random Popular Matchings with Incomplete Preference Lists2019

    • Author(s)
      Ruangwises Suthee、Itoh Toshiya
    • Journal Title

      Journal of Graph Algorithms and Applications

      Volume: 23 Pages: 815-835

    • DOI

      10.7155/jgaa.00513

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Competitive Analysis for the Multi-Objective Time Series Search Problem2019

    • Author(s)
      ITOH Toshiya、TAKEI Yoshinori
    • Journal Title

      IEICE Trans. Fundamentals

      Volume: E102.A Issue: 9 Pages: 1150-1158

    • DOI

      10.1587/transfun.e102.a.1150

      10.1587/transfun.E102.A.1150

    • NAID

      130007699482

    • ISSN
      0916-8508, 1745-1337
    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stable Noncrossing Matchings2019

    • Author(s)
      Ruangwises Suthee、Itoh Toshiya
    • Journal Title

      Proc. of International Workshop on Combinatorial Algorithms

      Volume: LNCS 11638 Pages: 405-416

    • DOI

      10.1007/978-3-030-25005-8_33

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] AND Protocols Using only Uniform Shuffles2019

    • Author(s)
      Ruangwises Suthee、Itoh Toshiya
    • Journal Title

      International Computer Science Symposium in Russia

      Volume: LNCS 11532 Pages: 349-358

    • DOI

      10.1007/978-3-030-19955-5_30

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Unpopularity Factor in the Marriage and Roommates Problems2019

    • Author(s)
      Ruangwises Suthee、Itoh Toshiya
    • Journal Title

      International Computer Science Symposium in Russia

      Volume: LNCS 11532 Pages: 337-348

    • DOI

      10.1007/978-3-030-19955-5_29

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bounded depth circuits with weighted symmetric gates: Satisfiability, lower bounds and compression2019

    • Author(s)
      Sakai Takayuki、Seto Kazuhisa、Tamaki Suguru、Teruyama Junichi
    • Journal Title

      Journal of Computer and System Sciences

      Volume: 印刷中 Pages: 87-103

    • DOI

      10.1016/j.jcss.2019.04.004

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Improved Fixed-Parameter Algorithm for Max-Cut Parameterized by Crossing Number2019

    • Author(s)
      Kobayashi Yasuaki、Kobayashi Yusuke、Miyazaki Shuichi、Tamaki Suguru
    • Journal Title

      Proceedings of IWOCA 2019

      Volume: 30 Pages: 327-338

    • DOI

      10.1007/978-3-030-25005-8_27

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Polynomial size linear programs for problems in P2019

    • Author(s)
      David Avis, David Bremner, Hans Tiwary and Osamu Watanabe
    • Journal Title

      Discrete Applied Mathematics

      Volume: online Pages: 22-39

    • DOI

      10.1016/j.dam.2019.03.016

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Periodic Fourier representation of Boolean functions2019

    • Author(s)
      Ryuhei Mori
    • Journal Title

      Quantum Information & Computation

      Volume: 19

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fine-grained quantum computational supremacy2019

    • Author(s)
      Tomoyuki Morimae and Suguru Tamaki
    • Journal Title

      Quantum Information & Computation

      Volume: 19

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An improvement of the algorithm of Hertli for the Unique 3SAT problem2019

    • Author(s)
      Tong Qin, Osamu Watanabe
    • Journal Title

      Theoretical Computer Science

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A space-efficient separator algorithm for planar graphs2019

    • Author(s)
      Ryo Ashida, Sebastian Kuhnert, Osamu Watanabe
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications, and Computer Science

      Volume: 印刷中

    • NAID

      130007699441

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodic Fourier representation of Boolean functions2019

    • Author(s)
      Ryuhei Mori
    • Journal Title

      Quantum Information and Computation

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum Query Complexity of Unitary Operator Discrimination2019

    • Author(s)
      KAWACHI Akinori、KAWANO Kenichi、LE GALL Francois、TAMAKI Suguru
    • Journal Title

      IEICE Trans. Inf. & Syst.

      Volume: E102.D Issue: 3 Pages: 483-491

    • DOI

      10.1587/transinf.2018fcp0012

      10.1587/transinf.2018FCP0012

    • NAID

      130007606941

    • ISSN
      0916-8532, 1745-1361
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Depth Two (<i>n</i>-2)-Majority Circuits for <i>n</i>-Majority2018

    • Author(s)
      Kazuyuki Amano and Masafumi Yoshida
    • Journal Title

      IEICE Trans. Fundamentals

      Volume: E101-A-9 Issue: 9 Pages: 1543-1545

    • DOI

      10.1587/transfun.e101.a.1543

      10.1587/transfun.E101.A.1543

    • NAID

      130007479524

    • ISSN
      0916-8508, 1745-1337
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Random popular matchings with incomplete preference lists2018

    • Author(s)
      Suthee Ruangwises, Toshiya Itoh
    • Journal Title

      Proc. of the 12th International Conference and Workshops on Algorithms

      Volume: - Pages: 106-118

    • DOI

      10.1007/978-3-319-75172-6_10

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Aggregating Two Metrics with Relaxed Triangle Inequalities by the Weighted Harmonic Mean2018

    • Author(s)
      Toshiya Itoh, Yoshinori Takei
    • Journal Title

      IEICE Trans. Fundamentals

      Volume: E101.A Issue: 9 Pages: 1404-1411

    • DOI

      10.1587/transfun.e101.a.1404

      10.1587/transfun.E101.A.1404

    • NAID

      130007479454

    • ISSN
      0916-8508, 1745-1337
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Approximation Guarantees for the Minimum Linear Arrangement Problem by Higher Eigenvalues2018

    • Author(s)
      Tamaki Suguru、Yoshida Yuichi
    • Journal Title

      ACM Transactions on Algorithms

      Volume: 14 Pages: 1-13

    • DOI

      10.1145/3228342

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gate elimination: Circuit size lower bounds and #SAT upper bounds2018

    • Author(s)
      Golovnev Alexander、Kulikov Alexander S.、Smal Alexander V.、Tamaki Suguru
    • Journal Title

      Theoretical Computer Science

      Volume: 719 Pages: 46-63

    • DOI

      10.1016/j.tcs.2017.11.008

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Non-black-box worst-case to average-case reductions within NP2018

    • Author(s)
      Shuichi Hirahara
    • Journal Title

      59th IEEE Annual Symposium on Foundations of Computer Science (FOCS 2018)

      Volume: - Pages: 247-258

    • DOI

      10.1109/focs.2018.00032

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Presentation] Space efficient separator algorithms for planar graphs2020

    • Author(s)
      Osamu Watanabe
    • Organizer
      The 14th Int'l Conf. and Workshops on Algorithms and Computation
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Space Efficient Separator Algorithms for Planar Graphs2020

    • Author(s)
      Watanabe Osamu
    • Organizer
      Algorithms and Computation - 14th International Conference
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] T-テトロミノを用いた平面アンチスライドパズルの最少ピース数について2020

    • Author(s)
      木村 健斗,天野 一幸,荒木 徹也
    • Organizer
      電子情報通信学会総合大会 COMP学生シンポジウム
    • Related Report
      2019 Annual Research Report
  • [Presentation] 多数決関数を計算する2段の多数決回路における総入次数の上下界2020

    • Author(s)
      横川 拓哉,尾島 康浩,天野 一幸
    • Organizer
      2019年度冬のLAシンポジウム
    • Related Report
      2019 Annual Research Report
  • [Presentation] SATソルバーによる複数の折り方を持つ箱の展開図の探索2020

    • Author(s)
      只木 莉緒奈,天野 一幸
    • Organizer
      情報処理学会 アルゴリズム研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 数理計画を用いた閾値回路の計算複雑さの解析2020

    • Author(s)
      天野 一幸
    • Organizer
      情報処理学会 アルゴリズム研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] ランダム関数におけるk-OR問題の量子アルゴリズム2020

    • Author(s)
      中川 毅紀,森 立平
    • Organizer
      2019年度冬のLAシンポジウム
    • Related Report
      2019 Annual Research Report
  • [Presentation] NPの最悪時及び平均時計算量について2020

    • Author(s)
      平原 秀一
    • Organizer
      電子情報通信学会総合大会 COMP学生シンポジウム
    • Related Report
      2019 Annual Research Report
  • [Presentation] アンチスライドパズルの解析2019

    • Author(s)
      木村 健斗,天野 一幸,荒木 徹也
    • Organizer
      電子情報通信学会 コンピュテーション研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 多数決関数を計算する2段の多数決回路2019

    • Author(s)
      尾島 康浩,横川 拓哉,天野 一幸
    • Organizer
      電子情報通信学会 コンピュテーション研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 5以上の素数次元におけるマジック状態蒸留プロトコルの等価性の条件2019

    • Author(s)
      近藤 泰大,森 立平
    • Organizer
      量子情報技術研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] グラフ彩色問題の指数時間量子アルゴリズム2019

    • Author(s)
      清水 一矢,森 立平
    • Organizer
      量子情報技術研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Beating brute force for systems of polynomial equations over finite fields2019

    • Author(s)
      Suguru Tamaki
    • Organizer
      MPI-INF and MPI-MiS joint workshop on Theoretical Computer Science and Algebraic Geometry
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The robustness of LWPP and WPP, with an application to graph reconstruction2018

    • Author(s)
      Edith Hemaspaandra, Lane A. Hemaspaandra, Holger Spakowski, Osamu Watanabe
    • Organizer
      The 43rd International Symposium on Mathematical Foundations of Computer Science
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] NP-hardness of minimum circuit size problem for OR-AND-MOD circuits2018

    • Author(s)
      Shuichi Hirahara, Igor Carboni Oliveira, and Rahul Santhanam
    • Organizer
      The 33rd Computational Complexity Conference
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Depth two majority circuits for majority and list expanders2018

    • Author(s)
      Kazuyuki Amano
    • Organizer
      The 43rd International Symposium on Mathematical Foundations of Computer Science
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Away from rivals2018

    • Author(s)
      Kazuyuki Amano, Shin-ichi Nakano
    • Organizer
      The 30th Canadian Conference on Computational Geometry
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research

URL: 

Published: 2018-04-23   Modified: 2022-12-28  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi