Developing computer-assisted methods for proving computational intractability

2015 Fiscal Year Final Research Report

• Project/Area Number: 24500006
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Gunma University
• Principal Investigator: Kazuyuki Amano 群馬大学, 大学院理工学府, 教授 (30282031)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 計算量理論 / 論理関数 / 論理回路 / 下界 / 計算機援用証明 / 数理計画

Outline of Final Research Achievements

On the representation of Boolean functions by polynomial threshold functions (PTF, in short), we showed that the property called XOR Lemma, which has shown to be true for PTF degree, is not hold if we consider other important measures such as PTF weight or length. We developed a method for reducing the problem of analyzing the non-deterministic communication complexity of Boolean functions to the one of constructing a decomposition of a certain graph, and gave an improved lower bound on the complexity of the clique versus independent set problem. In addition, we gave a new algorithm for satisfiability problem for a certain class of threshold circuits.

Free Research Field

計算量理論