Author: Bob Durrett
Date: 19:39:32 11/16/02
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On November 16, 2002 at 22:08:55, Christophe Theron wrote: >On November 16, 2002 at 22:00:27, Bob Durrett wrote: > >> >>I was thinking it might be *fun* to create a machine which does nothing more >>than create legal move sequences from some preset legal chess position. These >>sequences might be dumped into a large part of RAM for later copy to a hard disk >>or printout. >> >>The key idea I'm toying with is to represent a chess position by a listing of >>legal moves. Whenever a new move is made [by the person (or thing) playing >>against the machine, or by the machine if it's playing against itself,] then the >>machine would do nothing more than modify that listing (plus copy the move >>representation to a temporary storage place in RAM). The new listing of legal >>moves would then represent the new position. The key idea is to represent a >>position by a listing of legal moves. When a move is made, there is a "from" >>square and a "to" square. Only consequences of changes made on these two >>squares would have to be considered to modify the legal move list. >> >>Then, to make it more interesting, a really fast random number generator would >>be used to select one of the resulting legal moves. If the machine were playing >>against itself, the sequences of moves should be generated very quickly. How >>quickly? >> >>In the beginning, I am only interested in the time it would take to modify that >>listing. The machine could play both sides, removing the need for >>time-consuming input/output. After generating a legal move sequence ending in >>mate, it would then start working on the next legal move sequence. After a >>million or so moves were made, then the time required could be divided by the >>number of moves. That resulting time per move that I'm asking about. Rather >>than worry about the fact that some computers are faster than others, maybe the >>best bet would be to express it as number of clock cycles per move. A modern >>high-end processor should be assumed. >> >>Each sequence would be what two "really dumb" chessplayers would produce if they >>knew how to produce legal moves but knew NOTHING at all else about chess. >> >>P.S. Is there a better way? >> >>Bob D. > > > >Don't you need to prove first that two different chess positions will always >have a different legal moves list? And that there exist no move list that could >be associated with two different chess positions? > > > > Christophe Here is an outline of a proof that there exists one and only one legal move listing for each and every legal position. The proof has two parts: (a) Proof that each legal move list produced does represent at least one legal position. (b) Proof that no legal position can be represented by two or more distinct legal move list. (a) The initial position is legal. the move made is legal. The resulting position is legal. The resulting legal move list represents that legal position at least. (b) A legal move list is generated from a legal move made in a legal position. The process as described can produce only one legal move list [because of the unexplained details.] That legal move list is unique in the sense that it is the only one that could be produced by the described process. The above is not a proof. It is only a sketch or outline of a proof. To prove that a 1:1 correspondence is needed for the intended purposes, it might suffice just to give a single counter-example. Bob D.
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