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Consider the following problem: In a situation like the one described in Figure 5,
we would like the robot to move the box from room A to room B. Also, we assume
that the box is too big to fit through the opening that connects the two rooms, but the
robot doesn't know this! (The same problem with the same assumption is considered
in , where a method based on reflective planning is developed to solve it). If we
use the individual K-lines of Figure 5 or Figure 6 (i.e., without those K-lines being
merged), then there are two possible solutions, S1 and S2: (S1) start from K-line KL1
and produce the sequence 11-12-13-14-15-16; (S2) start from K-line KL2 and pro-
duce the sequence 21-22-23-24-25. Note, S1 will fail at step 14 since the box does not
fit through the opening between rooms A and B; and S2 is not applicable , since the
starting point, 21, is outside the domain of the robot problem! Therefore, the system
of two separate K-lines KL1 and KL2 is incapable of solving this problem.
However, if we consider the same K-lines but with the K-lines being merged, (as
shown in Figure 7), then we can generate 4 (instead of 2) possible solutions: (G1)
start from K-line KL1 and produce the sequence 11-12-13-14-15-16; (G2) start from
K-line KL1 and produce the sequence 11-12-23-15-16; (G3) start from K-line KL2
and produce the sequence 21-12-23-15-16; (G4) start from K-line KL2 and produce
the sequence 21-12-13-14-15-16. Note, solutions G1 and G3 are the same as S1 and
S2, respectively, and therefore either fail or are not applicable. Solution G4 is also not
applicable, since it starts from K-line KL2. However, solution G2 is applicable (since
it starts from K-line KL1) and it will also succeed ! Note, G2 is also the result of com-
bining 2 K-lines, KL1 and KL2 and G2 is not available as an option if the two K-lines
are not merged.
3.2 Application 2: Machine Learning
AKL can be useful in machine learning scenarios. We illustrate our case for a simple
board game - Tic-Tac-To. The method can be applied to any strategy game, such as
chess, go, etc.
The game of Tic-Tac-To (TTT) is played by 2 players, PX and PO, using a 3x3
board, as shown in Figure 8.
Fig. 8. Typical board for Tic-Tac-To game