Author: Uri Blass
Date: 11:37:01 12/12/02
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On December 12, 2002 at 14:08:22, Dann Corbit wrote: >On December 12, 2002 at 12:47:20, J. Wesley Cleveland wrote: >[snip] >>You are the one that said you could prove that chess was not currently solvable, >>which means others can speculate and you have to prove them wrong. > >I was wrong. See some other message I wrote elsewhere in this thread in answer >to Heiner. >[snip] >>The proof takes only a few steps. Define king confined in a rectangle n,m as >>queen on square n+1,m+1, king in the rectangle not adjacent to the queen, and >>opposing king outside the rectangle n+1,m+1. Prove if the king is confined in a >>rectangle of 3,1 or 3,2, it is checkmate. Prove if the king is confined in a >>rectangle of n,1, you can force it to be confined in a rectangle of n-1,1. Prove >>if the king is confined in a rectangle of n,m, you can force it to be confined >>in a rectangle of n-1,m or n,m-1. Prove that you can confine the king in a >>rectangle. QED. > >This proof will take exactly the same number of steps to complete as the tree >search. Hence it is an implicit tree. > >I could just post a ten line minimax algorithm and say: >"Chess is solved." > >We can easily show that the algorithm terminates. I can give you a simple example when it is possible to prove things without a tree. [D]k7/P2ppp2/K7/8/8/8/7P/8 w - - 0 1 I can see mate in 5 without calculating all the tree 1.h4,2.h5 3.h6,4.h7,5.h8R# a stupid computer program(and I believe that all of the available programs are) need to calculate a lot of lines(1.h4 f5,1.h4 f6,....) Humans do not need to calculate them because they can see that the white pawn promotes before the black pawns and they can see that the place of the black pawns is not relevant when they cannot promote. It is simple to prove it by a tree of classes of positions and not a tree of positions. Another simple example [D]7k/8/1p1p1p1p/pPpPpPpP/P1P1P1P1/8/8/6KR w - - 0 1 It is simple to prove that it is a draw without tree or tablebases. Uri
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