On Exact Algorithms for Branching Program Satisfiability Problems by Approaches for Proving Lower Bounds

2023 Fiscal Year Final Research Report

• Project/Area Number: 18K18003
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60010:Theory of informatics-related
• Research Institution: University of Hyogo
• Principal Investigator: Teruyama Junichi 兵庫県立大学, 情報科学研究科, 准教授 (40709862)
• Project Period (FY): 2018-04-01 – 2024-03-31
• Keywords: 充足可能性問題 / 分岐プログラム / 厳密アルゴリズム / 回路計算量

Outline of Final Research Achievements

To solve the P vs. NP problem, which is the most important problem in theoretical computer science, we studied the separation of computational classes by providing a satisfiability algorithm for branching programs. Mainly, we investigated designing algorithms for branching programs with constant width using the lower bound proof technique.
In this research, we succeeded in designing an algorithm for the satisfiability problem of branching programs of linear size and width two. It runs faster than the brute forth search and uses the lower bound proof technique as a subroutine.

Free Research Field

理論計算機科学

Academic Significance and Societal Importance of the Research Achievements

本研究での成果は計算量理論およびアルゴリズム理論の両分野に関連する成果といえる．計算量理論の分野においては，計算量クラスの分離という基礎的な問題に向けた第一歩と与えた．アルゴリズム理論分野においては，分岐プログラムサイズの下界証明技法を取り入れた新しい重曹可能性判定アルゴリズムの設計技法を与えた．