License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2018.3
URN: urn:nbn:de:0030-drops-87944
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8794/
Abel, Zachary ;
Bosboom, Jeffrey ;
Demaine, Erik D. ;
Hamilton, Linus ;
Hesterberg, Adam ;
Kopinsky, Justin ;
Lynch, Jayson ;
Rudoy, Mikhail
Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible
Abstract
We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a path in a rectangular grid graph from a start vertex to a destination vertex. The different puzzle types place different constraints on the path: preventing some edges from being visited (broken edges); forcing some edges or vertices to be visited (hexagons); forcing some cells to have certain numbers of incident path edges (triangles); or forcing the regions formed by the path to be partially monochromatic (squares), have exactly two special cells (stars), or be singly covered by given shapes (polyominoes) and/or negatively counting shapes (antipolyominoes). We show that any one of these clue types (except the first) is enough to make path finding NP-complete ("witnesses exist but are hard to find"), even for rectangular boards. Furthermore, we show that a final clue type (antibody), which necessarily "cancels" the effect of another clue in the same region, makes path finding Sigma_2-complete ("witnesses do not exist"), even with a single antibody (combined with many anti/polyominoes), and the problem gets no harder with many antibodies.
BibTeX - Entry
@InProceedings{abel_et_al:LIPIcs:2018:8794,
author = {Zachary Abel and Jeffrey Bosboom and Erik D. Demaine and Linus Hamilton and Adam Hesterberg and Justin Kopinsky and Jayson Lynch and Mikhail Rudoy},
title = {{Who witnesses The Witnessl Finding witnesses in The Witness is hard and sometimes impossible}},
booktitle = {9th International Conference on Fun with Algorithms (FUN 2018)},
pages = {3:1--3:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-067-5},
ISSN = {1868-8969},
year = {2018},
volume = {100},
editor = {Hiro Ito and Stefano Leonardi and Linda Pagli and Giuseppe Prencipe},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8794},
URN = {urn:nbn:de:0030-drops-87944},
doi = {10.4230/LIPIcs.FUN.2018.3},
annote = {Keywords: video games, puzzles, hardness}
}
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Keywords: |
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video games, puzzles, hardness |
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Collection: |
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9th International Conference on Fun with Algorithms (FUN 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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04.06.2018 |
