Re: Mathematical approach

["Hans F. Zschintzsch" <hfz@xxxxxxxxxxx>]

Lionel Fumery schrieb:

> ...
> Could anybody help me in this mathematical approach of Go ?
> 
> G = the goban, a 19x19 Matrix
> t = a temporel index
> f = your Go engine (mine doesn't work :))
> 
> G(t+1) = f ( G(t) )
> 
> To find f, we need a "quality" function, Q :
> Q(G(t+1)) must be superior to Q(G(t)) (for the same player, of course)
> 
> My question :
>     So, what can I use for this Q function ? Any Idea ? The sum of my
> influences ?

A mathematical approach must be much more precise. Please be 
more explicit.

You say G is the board? (or the position?). On the other hand
G seems to be a function of t (t=time?). What is the domain? 
What is the range? You probably mean G(t+1) is the position 
which follows G(t) after Black or White made a move in G(t)? 
If so, then G(t+1) is dependant of the move Black or White 
choses. I would then prefere to write 

    G(Bx)   or   G+Bx

for the position resulting from a Black play on x in G.

The set of potential follow-up positions of G would then be

    F(G) = { G+Bx | x \in valid_moves_in(G) }

Similar your f. Is f a function at all? If Yes, what is the 
domain and range of f? If not, what is it then? 

My move generator e.g. selects at random from a set of valid 
moves rated high (by some other function) in a given position. 
So my "Go engine" does not produce always the same follow-up 
position when "working" on G.

The quality function Q: Again no domain and range is given.
>From your text i got the impression you want to rate f, and 
you want to to have Q(f')>Q(f) if f' produces better moves.

However you wrote "Q(G(t+1)) must be superior to Q(G(t))"
which look like rating positions instead of move_generating
functions.

> Thank you for any comment/idea.

Just my 2 cents.

Hans

PS. I might have misinterpreted what you wanted to say. If 
my comment is not of help please just ignore it. My point is 
that to be more precise (especially if the subject contains
the words "Mathematical approach") avoids the reader having 
to do the guesswork, which - at least on my part - generated 
some sort of frustration.