Question

For the Grasses-planting problem, there are THREE squares that the farmer robot can be located and three possible actions Move Left (L), Move Right (R) and Plant-grass (P). Move Left (Right) in the Left-Most (Right-Most) square will stay in the same square. A Square can be either "with grasses" or "empty" . the objective of the farmber robot is to plant grasses on all the squares. An example state that the farmer robot located at the LEFT square and there are grasses on both the CENTER and the Right squares is given below.

(a) Give an Action Sequence such that the agent is able to complete the task if the initial state is the same as the given example above. (b) Compute the number of all possible states for this problem (c) Draw the STATE SPACE GRAPH for this problem (remark: use symbols to replace pictures d) State an Action Sequence such that the agent must be able to complete the task without any knowledge of the current state. Question V (2006) Oradea Neamt

Answer 1

a) Action sequence to complete the task for the above example:

P

Explanation: As all the other squares are planted it is the only action to plant grass.

b) There are 24 states considering robots position

0- Represents empty(without grass)

1- Represents with grass

R- Represents robot

R0- Represents robot without grass

R1-Represents robot with grass

possible states are:

1) R0, 0, 0

2) 0, R0, 0

3) 0, 0, R0

4) R0, 1, 1

5) 1, R0, 1

6) 1, 1, R0

7) R0, 1, 0

8) 1, R0, 0

9) 1, 0, R0

10) R0, 0, 1

11) 0, R0, 1

12) 0, 1, R0

13) R1, 0, 0

14) 0, R1, 0

15) 0, 0, R1

16) R1, 1, 1

17) 1, R1, 1

18) 1, 1, R1

19) R1, 1, 0

20) 1, R1, 0

21) 1, 0, R1

22) R1, 0, 1

23) 0, R1, 1

24) 0, 1, R1

c)$q1\overset{l/l->s}{\rightarrow}q2\overset{p/\varepsilon }{\rightarrow}q3\overset{r}{\rightarrow}q4\overset{p/\varepsilon }{\rightarrow}q5\overset{r}{\rightarrow}q6\overset{p/\varepsilon }{\rightarrow}q7\overset{s}{\rightarrow}q8$

q1- is the initial state and it moves to left until it gets stop( represents to move left and represents stop).

q2- is the left most side of farm.

q3- it is a state where actions of plant grass() only if land is empty else it moves to another state without performing operation($\varepsilon$).

q4- it is a new state after moving to right().

these states are repeated in a similar way for others    

gb, gb,q

- represents final state where all 3 blocks are filled with grass

  

d)These is the action sequence which is independent of state

L,L,L,P,R,P,R,P

L- represents move left

P- represents plant grass

R- represents move right

-> no matter where the robot is present it comes to left most position after these sequence L,L,L

->P represents to plant grass if it is empty or filled with grass.

->R action helps to move right.

these sequence is independent of the state.

Hope it is clear please comment for queries.