Author: Angrim
Date: 12:21:35 12/11/02
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On December 10, 2002 at 18:24:47, Bob Durrett wrote: >On December 10, 2002 at 17:55:51, Dann Corbit wrote: > ><snip> > >>To solve chess you must store at least the square root of nodes of the solution >>tree. Considering the half move clock and castle rights, it easily exhausts any >>possibility of solution. > ><snip> > >I'm not sure what it is you are calling a "solution tree," but some [Uri, etc.] >have expressed the expectation that new undiscovered search [& position >evaluation] algorithms of the future will greatly decrease the number of nodes >that must be examined. The practical limitations for such improvements are >unclear. In the limit, the only nodes that would be examined would be in a >single branch, assuming all nodes have only one "best move." The number of >nodes in such a branch would be very manageable. In cases where two or moves >are equally good from a single node, then maybe the pruned tree would be >slightly more complex, but still manageable. Maybe that's what you are calling >a "solution tree"? > >Is it possible to establish the absolute limits for pruning and similar >"tricks"? Could it then be proven that the resulting tree would be too big to >analyze? > >Perhaps the real problem is uncertainty. There may be some sort of "Uncertainty >Principle" at work here. Maybe one can never be absolutely sure that the nodes >examined were properly analyzed to find the best move(s). Whether or not a move >is the best move may be something that must be expressed as a probability and >not an absolute certainty. > >Bob D. The solution tree is the tree of all positions whose value needs to be known to prove the value of the position being proven. For the case of proving that white wins a position, this tree would have to have *all* possible moves by black for each position with black to move, and *a* winning move for white for each position with white to move. Hope that clears it up a little. Angrim
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