Exploring the Limits of Computation from the Statistical Physics

2016 Fiscal Year Final Research Report

• Project Area: A multifaceted approach toward understanding the limitations of computation
• Project/Area Number: 24106008
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Watanabe Osamu 東京工業大学, 情報理工学院, 教授 (80158617)
• Co-Investigator(Kenkyū-buntansha): 安藤 映 崇城大学, 情報学部, 助教 (20583511) ; 伊東 利哉 東京工業大学, 情報理工学研究科, 教授 (20184674) ; 小柴 健史 埼玉大学, 理工学研究科, 教授 (60400800) ; 山本 真基 成蹊大学, 理工学部, 准教授 (50432414) ; 森 立平 東京工業大学, 情報理工学研究科, 助教 (60732857)
• Co-Investigator(Renkei-kenkyūsha): KABASHIMA Yoshiyuki 東京工業大学, 情報理工学院, 教授 (80260652) ; HUKUSHIMA Koji 東京大学, 総合文化研究科, 准教授 (80282606)
• Research Collaborator: Krzakala Florent Ecole Superieure de Physique et Chimie Industrielle ; Zdeborova Lenka CNRS, Institute of Theoret. Physics at CEA ; Zhou Haijun Chinese Academy of Sci., Inst. of Theoret. Physics
• Project Period (FY): 2012-06-28 – 2017-03-31
• Keywords: 計算困難さの解析 / 計算困難さの相転移 / 解空間の構造 / 解の数え上げ問題

Outline of Final Research Achievements

We investigated computational problems studied in the statistical physics for developing a new approach in computational complexity theory. We examined a framework proposed in the statistical physics for understanding the computational hardness transition phenomena, and we discovered and mathematically proved a new type of hardness transition, which lead us to propose a new and robust framework for investigating the computational hardness transitions. This framework can be used as a new basis of discussing the security of cryptographic primitives. We also studied the structure of solutions and the number of solutions of various computational problems that have been discussed in the statistical physics, and found several fundamental properties for developing efficient algorithms for solving these problems.

Free Research Field

計算の理論