Figure drawn by course staff based on http://simon.bailey.at/random/kaye.minesweeper.pdf
Minesweeper Consistency isNP-complete [Kaye 2000]
NOT
Phase changer(2 NOTs)
𝑥𝑥 𝑥𝑥𝑥𝑥 𝑥𝑥 𝑥𝑥𝑥𝑥 𝑥𝑥𝑥𝑥𝑥𝑥
𝑥𝑥𝑥𝑥 𝑥𝑥𝑥𝑥𝑥𝑥 𝑥𝑥 𝑥𝑥𝑥𝑥 𝑥𝑥𝑥𝑥
𝑥𝑥 𝑥𝑥
𝑥𝑥 𝑥𝑥
Presenter
Presentation Notes
Figure drawn by course staff based on http://simon.bailey.at/random/kaye.minesweeper.pdf
Minesweeper Consistency isNP-complete [Kaye 2000]
AND
turn
𝑥𝑥𝑥𝑥𝑥𝑥
𝑥𝑥
𝑥𝑥𝑥𝑥
𝑥𝑥
𝑧𝑧
𝑥𝑥𝑥𝑥
𝑥𝑥
𝑥𝑥
𝑧𝑧𝑧𝑧
𝑧𝑧
𝑧𝑧𝑧𝑧 𝑧𝑧
𝑥𝑥 𝑥𝑥𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑡𝑡 𝑡𝑡𝑡𝑡 𝑡𝑡
𝑡𝑡
𝑡𝑡
𝑡𝑡
𝑡𝑡
Presenter
Presentation Notes
Figure drawn by course staff based on http://simon.bailey.at/random/kaye.minesweeper.pdf
Minesweeper Consistency isNP-complete [Kaye 2000]
crossover
XOR
[Goldschlager 1977]
Presenter
Presentation Notes
Figures 11 and 12 of http://simon.bailey.at/random/kaye.minesweeper.pdf which in turn is based on http://dx.doi.org/10.1145/1008354.1008356
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
turn gadgetwire gadget terminator gadget
𝑥𝑥 𝑥𝑥
𝑥𝑥
𝑥𝑥
𝑥𝑥 𝑥𝑥
Presenter
Presentation Notes
Figure drawn by course staff based on http://dx.doi.org/10.1007/s00283-011-9256-x
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
OR gate
NOT gate shifter gadget
𝑥𝑥 𝑥𝑥𝑥𝑥 𝑥𝑥
𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥
𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥
Presenter
Presentation Notes
Figure drawn by course staff based on http://dx.doi.org/10.1007/s00283-011-9256-x
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
split gadget
crossover gadget
NOT
shiftershifter
𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥𝑥𝑥 𝑥𝑥𝑥𝑥
𝑥𝑥𝑥𝑥
𝑥𝑥
𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥
𝑥𝑥 𝑥𝑥
𝑣𝑣
𝑣𝑣𝑣𝑣
𝑣𝑣𝑣𝑣
𝑣𝑣𝑣𝑣
𝑣𝑣
𝑥𝑥 𝑥𝑥
Presenter
Presentation Notes
Figure drawn by course staff based on http://dx.doi.org/10.1007/s00283-011-9256-x
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
NAND
alternative crossover
gadget
Presenter
Presentation Notes
Figures 11 and 12 of http://simon.bailey.at/random/kaye.minesweeper.pdf which in turn is based on http://dx.doi.org/10.1145/1008354.1008356 Plus https://commons.wikimedia.org/wiki/File:NAND_from_NOR.svg#mediaviewer/File:NAND_from_NOR.svg
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
Presenter
Presentation Notes
Figure 7 of http://dx.doi.org/10.1007/s00283-011-9256-x