STATE MACHINES IN ARTIFICIAL INTELLIGENCE

mathematical representation that consists in formulas about possibile moves of
pieces, and concept about the winning or losing. After we have the mathematical
representation is evident that we can apply all mathematic theories, proofs and
algebra.
We analize a chess final, the final of rook composed by the interaction of two
pieces, king and rook of a colour, and the only king of the opponent. The formulas
express that the possibile moves are :
Possible Move of King:
X k t1=X k t∏ 1
b
a
−1∗X j ∗T :1 X k t18
Y k t1=Y k t∏ −1∗Y j∗T :1Y k t18
1
with a∈[1,2]
with b∈[1,2]
with 1 X jY j2with X j∈[0,1]∧Y j∈[0,1] with T ∈[0,1]
a indicate the direction of moving to the left or to the right
b indicate the direction of up or down movement
X j indicate if we want to move on the selected direction to the left or to the
right
Y j indicates if we want to move on the selected direction up or down
1 X j Y j 2 means that we must move in one of the selected directions
T indicates if we can move or if the opponent can move
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