Author: Dann Corbit
Date: 16:36:21 12/10/02
Go up one level in this thread
On December 10, 2002 at 19:16:06, Ingo Lindam wrote: >On December 10, 2002 at 18:54:33, Dann Corbit wrote: > >>On December 10, 2002 at 18:44:55, Ingo Lindam wrote: >> >>>On December 10, 2002 at 18:30:42, Dann Corbit wrote: >>> >>>>If I have a king and a rook verses a king, I can store a perfect solution to the >>>>puzzle in a tree. I can use only sqrt(n) possible states to form the solution >>>>and the solution will be optimal. You may find another solution, but it will >>>>not be superior to mine in any way. >>> >>>Dann, >>>I am sure I can proof KR vs. K is won just using a pencil and a single sheet of >>>paper... >>> >>>do I get the fields price for that? >> >>Will it be a proof for an aribitrary position? Or a proof for an individual >>position? >> >>An example is *NOT* a proof. In order to *prove* something you must show that >>there are *ZERO* exceptions. >> >>Now, with a king, a rook and an opponent king, there are less than: >>64*63*62 possible positions (many of them being illegal positions). >> >>The total is therefore less than 249984 and the square root of that is 500. >> >>Will you provide a formal proof with less than 500 pieces of information in >>total that shows it will work for every conceivable board state? >> >>I know you are thinking of an algorithmic solution. But if you follow the >>algorithm, you will see that it forms a tree. From here: >>[D]8/8/2K5/R7/4k3/8/8/8 b - - >>The black king can move to: >>[D]8/8/2K5/R7/3k4/8/8/8 b - - >>[D]8/8/2K5/R7/8/3k4/8/8 b - - >>[D]8/8/2K5/R7/8/4k3/8/8 b - - >>[D]8/8/2K5/R7/8/5k2/8/8 b - - >>[D]8/8/2K5/R7/5k2/8/8/8 b - - >> >>You will need to provide a response to each one of these. It continues forward >>to solution. The moves are obvious, but what we are encoding is the tree. The >>optimal move will form the minimal tree, if we make it each time. >> >>We could use a tablebase, but to *form* the tablebase, we must have formed the >>search beforehand. > >But we don't need to show the shortest win to mate to show that we will mate the >black king by using a given algorithm. If we do not prove the shortest mate, then we will have to prove a longer one, won't we? Otherwise, we will not have proven anything. Algorithm proving is also a lot harder than most people think. That is why program proving is rarely performed. It's too expensive.
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