## 抄録

Fill-a-Pix is a pencil-and-paper puzzle, which is popular worldwide since announced by Conceptis in 2003. It provides a rectangular grid of squares that must be filled in to create a picture. Precisely, we are given a rectangular grid of squares some of which has an integer from 0 to 9 in it, and our task is to paint some squares black so that every square with an integer has the same number of painted squares around it including the square itself. Despite its popularity, computational complexity of Fill-a-Pix has not been known. We in this paper show that the puzzle is NP-complete, ASP-complete, and #P-complete via a parsimonious reduction from the Boolean satisfiability problem. We also consider the fewest clues problem of Fill-a-Pix, where the fewest clues problem is recently introduced by Demaine et al. for analyzing computational complexity of designing “good” puzzles. We show that the fewest clues problem of Fill-a-Pix is Σ_{2} ^{P} -complete.

本文言語 | 英語 |
---|---|

ページ（範囲） | 1490-1496 |

ページ数 | 7 |

ジャーナル | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

巻 | E102A |

号 | 11 |

DOI | |

出版ステータス | 出版済み - 2019 |

外部発表 | はい |

## !!!All Science Journal Classification (ASJC) codes

- 信号処理
- コンピュータ グラフィックスおよびコンピュータ支援設計
- 電子工学および電気工学
- 応用数学

## フィンガープリント

「NP-completeness of fill-a-Pix and σ_{2}

^{p}-completeness of its fewest clues problem」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。