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A Phase Transition in Minesweeper

Authors: Ross Dempsey and Charles Guinn

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

We study the average-case complexity of the classic Minesweeper game in which players deduce the locations of mines on a two-dimensional lattice. Playing Minesweeper is known to be co-NP-complete. We show empirically that Minesweeper exhibits a phase transition analogous to the well-studied SAT phase transition. Above the critical mine density it becomes almost impossible to play Minesweeper by logical inference. We use a reduction to Boolean unsatisfiability to characterize the hardness of Minesweeper instances, and show that the hardness peaks at the phase transition. Furthermore, we demonstrate algorithmic barriers at the phase transition for polynomial-time approaches to Minesweeper inference. Finally, we comment on expectations for the asymptotic behavior of the phase transition.

Cite as

Ross Dempsey and Charles Guinn. A Phase Transition in Minesweeper. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 12:1-12:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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  author =	{Dempsey, Ross and Guinn, Charles},
  title =	{{A Phase Transition in Minesweeper}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{12:1--12:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-127735},
  doi =		{10.4230/LIPIcs.FUN.2021.12},
  annote =	{Keywords: Complexity of Games, Minesweeper}
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