### 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 N^{2} 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 | |

Publication status | Published - 1995 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Cognitive Neuroscience
- Cellular and Molecular Neuroscience

### Cite this

*Neurocomputing*,

*8*(1), 43-49. https://doi.org/10.1016/0925-2312(94)00003-4

**A neural network algorithm for the no-three-in-line problem.** / Tsuchiya, Kazuhiro; Takefuji, Yoshiyasu.

Research output: Contribution to journal › Article

*Neurocomputing*, vol. 8, no. 1, pp. 43-49. https://doi.org/10.1016/0925-2312(94)00003-4

}

TY - JOUR

T1 - A neural network algorithm for the no-three-in-line problem

AU - Tsuchiya, Kazuhiro

AU - Takefuji, Yoshiyasu

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

KW - Hysteresis Mc-Culloch-Pitts neuron

KW - Neural network algorithm

KW - No-three-in-line

KW - Unsolved problem

UR - http://www.scopus.com/inward/record.url?scp=0029294475&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029294475&partnerID=8YFLogxK

U2 - 10.1016/0925-2312(94)00003-4

DO - 10.1016/0925-2312(94)00003-4

M3 - Article

AN - SCOPUS:0029294475

VL - 8

SP - 43

EP - 49

JO - Neurocomputing

JF - Neurocomputing

SN - 0925-2312

IS - 1

ER -