Challenge to Sigma-2P complete problems: moving up in the polynomial hierarchy

2023 Fiscal Year Final Research Report

• Project/Area Number: 22K19813
• Research Category: Grant-in-Aid for Challenging Research (Exploratory)
• Allocation Type: Multi-year Fund
• Review Section: Medium-sized Section 61:Human informatics and related fields
• Research Institution: Kyushu University
• Principal Investigator: Yokoo Makoto 九州大学, システム情報科学研究院, 教授 (20380678)
• Project Period (FY): 2022-06-30 – 2024-03-31
• Keywords: Σ2P完全問題 / MaxSAT / robust solution

Outline of Final Research Achievements

In this project, we examine algorithms for solving sigma-2P-complete problems, which belongs to a class of problems that is one step higher than NP-complete problems in polynomial hierarchy. More specifically, we prove that a problem for minimizing the effect of adversarial attacks, when an adversary can modify a part of solutions of a weighted partial Max satisfiability problem, is sigma-2P-complete. Furthermore, we develop an exact algorithm for solving it. This result is published in Pacific Rim International Conference on Artificial Intelligence (PRICAI-2022) as a full paper. Furthermore, we present this work at Symposium on Multi Agent Systems for Harmonization 2022 Winter Symposium (SMASH22), which is awarded as one of best papers.

Free Research Field

マルチエージェントシステム

Academic Significance and Societal Importance of the Research Achievements

特筆すべき点として，Σ2P完全と呼ばれる，多項式階層において困難さのレベルがNP完全問題よりも一段階上のクラスの問題に関して，近年発展が著しいSATソルバーと呼ばれる効率的な重み付き部分最大SAT問題を解くプログラムをサブルーチンとして用いて，現実的な時間内で最適解を得るアルゴリズムを開発したことがある．このような問題は，敵対者が存在する状況で，敵対者の妨害に対して頑健な解を求めるということに対応し，敵対者が存在するクリーク分割問題等，数多くの応用事例に適用可能である．