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DOI: 10.4230/LIPIcs.MFCS.2021.25
URN: urn:nbn:de:0030-drops-144657
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14465/
Buchin, Kevin ; Hagedoorn, Mart ; Kostitsyna, Irina ; van Mulken, Max
Dots & Boxes Is PSPACE-Complete
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Abstract
Exactly 20 years ago at MFCS, Demaine posed the open problem whether the game of Dots & Boxes is PSPACE-complete. Dots & Boxes has been studied extensively, with for instance a chapter in Berlekamp et al. Winning Ways for Your Mathematical Plays, a whole book on the game The Dots and Boxes Game: Sophisticated Child’s Play by Berlekamp, and numerous articles in the Games of No Chance series. While known to be NP-hard, the question of its complexity remained open. We resolve this question, proving that the game is PSPACE-complete by a reduction from a game played on propositional formulas.
BibTeX - Entry
@InProceedings{buchin_et_al:LIPIcs.MFCS.2021.25,
author = {Buchin, Kevin and Hagedoorn, Mart and Kostitsyna, Irina and van Mulken, Max},
title = {{Dots \& Boxes Is PSPACE-Complete}},
booktitle = {46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
pages = {25:1--25:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-201-3},
ISSN = {1868-8969},
year = {2021},
volume = {202},
editor = {Bonchi, Filippo and Puglisi, Simon J.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14465},
URN = {urn:nbn:de:0030-drops-144657},
doi = {10.4230/LIPIcs.MFCS.2021.25},
annote = {Keywords: Dots \& Boxes, PSPACE-complete, combinatorial game}
}
| Keywords: | Dots & Boxes, PSPACE-complete, combinatorial game | |
| Seminar: | 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 18.08.2021 |
