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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 [5], 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

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