Exploring the computational power of threshold circuits with the limited number of output patterns

2015 Fiscal Year Final Research Report

• Project/Area Number: 25330005
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Yamagata University
• Principal Investigator: Kei Uchizawa 山形大学, 理工学研究科, 准教授 (90510248)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 計算理論 / しきい値回路 / ニューラルネットワーク / 回路計算量理論

Outline of Final Research Achievements

We investigate the computational power of threshold circuits with the limited number of output patterns．We prove that there exists an explicit Boolean function such that any threshold circuit consisting of threshold gates with restricted weights requires an exponential number of output patterns. Our result thus implies that the number of output patterns can be strongly related to the computational power of threshold circuits and its weights of threshold gates. We also consider a discrete dynamical system defined on logic gates, and introduce a decision problem with regard to the output patterns on the system. We then show that the problem may belong to a complexity class of which few problems are known to be candidates of the members.

Free Research Field

計算理論