@MISC{Kaye_infiniteversions, author = {Richard Kaye}, title = {Infinite versions of minesweeper are Turing complete}, year = {} }

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this paper is my article [5] showing that the wellknown Minesweeper game is NP-complete. The proof was by making suitable minesweeper configurations simulate digital computers, with logic gates such as and and not gates. This is reminiscent of John Conway's game of life [2] which was proved to be Turing complete by similar means [1]. (For background information on Turing machines and computability please see just about any text book on these. I found the account by Wang [7] particularly enjoyable and can recommend it as it presents just about the right about of material needed here in a straightforward and not too technical manner.) It is reasonable to ask whether or not there is an version of Minesweeper

...er configurations simulate digital computers, with logic gates such as and and not gates. This is reminiscent of John Conway’s game of life [2] which was proved to be Turing complete by similar mean=-=s [1]-=-. (For background information on Turing machines and computability please see just about any text book on these. I found the account by Wang [7] particularly enjoyable and can recommend it as it prese...

...I 1 W 0 ¬ 0 W 1 N 2 0 2 N W 1 W N 3 N As is well-known, from nor gates and not gates, all the other standard logic gates can be constructed; planar circuits to do this were discovered by Goldschlager=-= [3]-=-, and a way to do this is indicated my the original paper on the NP-completeness of Minesweeper. For the final part of the proof that Turing machine computations can be 12sFigure 1: A Minesweeper comp...

...l of Mathematics and Statistics The University of Birmingham Birmingham B15 2TT R.W.Kaye@bham.ac.uk http://www.mat.bham.ac.uk/R.W.Kaye 15th August 2000 The starting point for this paper is my article =-=[5]-=- showing that the wellknown Minesweeper game is NP-complete. The proof was by making suitable minesweeper configurations simulate digital computers, with logic gates such as and and not gates. This is...

...e is NP-complete. The proof was by making suitable minesweeper configurations simulate digital computers, with logic gates such as and and not gates. This is reminiscent of John Conway’s game of lif=-=e [2]-=- which was proved to be Turing complete by similar means [1]. (For background information on Turing machines and computability please see just about any text book on these. I found the account by Wang...

...which was proved to be Turing complete by similar means [1]. (For background information on Turing machines and computability please see just about any text book on these. I found the account by Wang =-=[7]-=- particularly enjoyable and can recommend it as it presents just about the right about of material needed here in a straightforward and not too technical manner.) It is reasonable to ask whether or no...