As a side note, if you enjoy playing Minesweeper but don't like losing to a bad guess, you might want to try the implementation in Simon Tatham's puzzle collection:
Unlike most other implementations, it only generates boards that can be solved by logic, so you never need to guess; your first square is guaranteed to be safe and to reveal enough information to progress.
(IIRC, the algorithm used to pre-solve each generated level bottoms out in an exhaustive search, so I guess this game variant is still in NP.)
Figure 3 is incomplete; as the space depicted in it is not a valid board configuration. If either x or x' is false, then the respective 1s on the extreme sides will be invalid. This is either a crop of a real situation (in which we assume the wire repeats beyond the scope of the image), or an error.
It is a crop of a board containing a wire that extends beyond the area shown. It is not an error, although indicating (somehow - people's intuitions vary) that it's a crop would help.
http://www.chiark.greenend.org.uk/~sgtatham/puzzles/
Unlike most other implementations, it only generates boards that can be solved by logic, so you never need to guess; your first square is guaranteed to be safe and to reveal enough information to progress.
(IIRC, the algorithm used to pre-solve each generated level bottoms out in an exhaustive search, so I guess this game variant is still in NP.)