A neural network algorithm for the no-three-in-line problem

Kazuhiro Tsuchiya; Yoshiyasu Takefuji

doi:10.1016/0925-2312(94)00003-4

A neural network algorithm for the no-three-in-line problem

Kazuhiro Tsuchiya, Yoshiyasu Takefuji

Faculty of Environment and Information Studies

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The no-three-in-line problem is one of unsolved problems in number theorem. The goal of the no-three-in-line problem is to locate 2N points on an N × N squares array where no three points are in line. The proposed algorithm uses N² hysteresis McCulloch-Pitts neurons as the processing elements for the N × N array problem. Our neural network algorithm has discovered several different solutions for up to N = 25.

Original language	English
Pages (from-to)	43-49
Number of pages	7
Journal	Neurocomputing
Volume	8
Issue number	1
DOIs	https://doi.org/10.1016/0925-2312(94)00003-4
Publication status	Published - 1995 May

Keywords

Hysteresis Mc-Culloch-Pitts neuron
Neural network algorithm
No-three-in-line
Unsolved problem

ASJC Scopus subject areas

Computer Science Applications
Cognitive Neuroscience
Artificial Intelligence

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10.1016/0925-2312(94)00003-4

Cite this

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title = "A neural network algorithm for the no-three-in-line problem",

abstract = "The no-three-in-line problem is one of unsolved problems in number theorem. The goal of the no-three-in-line problem is to locate 2N points on an N × N squares array where no three points are in line. The proposed algorithm uses N2 hysteresis McCulloch-Pitts neurons as the processing elements for the N × N array problem. Our neural network algorithm has discovered several different solutions for up to N = 25.",

keywords = "Hysteresis Mc-Culloch-Pitts neuron, Neural network algorithm, No-three-in-line, Unsolved problem",

author = "Kazuhiro Tsuchiya and Yoshiyasu Takefuji",

note = "Funding Information: partially supported by Fuji Electric Co., Ltd. and TEPCO Science Foundation. author. Email: tsuchiya@axon.eeap.cwru.edu Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

year = "1995",

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A neural network algorithm for the no-three-in-line problem

Abstract

Keywords

ASJC Scopus subject areas

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