and/or graph search - wikimedia · 5a and/or graph 3 young won lim 14년 10월 27일 hanoi tower...

Young Won Lim14년 10월 27일

● Problem Reduction● Hanoi Tower● Monkey and Banana● AND/OR Graph Search

AND/OR Graph Search


Copyright (c) 2010 Young W. Lim.

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5A AND/OR Graph 3 Young Won Lim14년 10월 27일

Hanoi Tower – Problem Reduction

(1 1 1)

BA

C

1 2 3 1 2 3

BA

C

1 2 3BA

C

(1 2 2) (3 2 2)

(3 3 3)

1 2 3BA

C


Hanoi Tower – State Space

(1 1 1)

(1 1 2)

(1 3 2)

(1 3 3)

(2 3 3)

(2 3 1)

(2 2 1)

(2 2 2)

(1 1 3)

(1 2 3)

(1 3 1) (1 2 1)

(1 2 2)

(3 2 2)

(2 3 2) (3 2 3) (3 2 1)

(2 1 2) (1 3 1) (3 3 1)

(2 2 3) (2 1 3) (2 1 1) (3 1 1) (3 1 2) (3 3 2) (3 3 3)

ABC

BC

A

C

A

B

C

AB

C

AB

A

C

B

A

BC

BC

A

C

B

A

AC

B

AC

B

C

AB

AC

B

B

AC

A

B

C

B

AC

AC

B

A

BC

ABC

BC

A

B

C

A

AB

C

AB

C

B

A

C

A

BC

ABC

A B

C


Key Operator

(1 1 1)

(1 2 2) (3 2 2)

(3 3 3)

ABC

C

AB

ABC

A B

C

Primitive Problem

Key Operator


AND/OR Graph

(1 1 1)

(1 2 2) (3 2 2)

(3 3 3)

ABC

C

AB

ABC

A B

C

Key Operator

Problem A

Problem B

Problem C

Problem D A

C DB

B AND C AND D


AND/OR Graph – Terminal Node

A

C DB

E OR F

(1 1 1)

(1 2 2) (3 2 2)

(3 3 3)

ABC

C

AB

ABC

A B

C

Primitive Problem

Key Operator

E F G H

G OR H OR ...

Terminal Node


Monkey and Banana

goto

pushboxclimbbox

grasp


Monkey and Banana - State

(w, x, y, z)

w: the position of the monkey (horizontal, vertical)x: monkey on top of the box (1 or 0)y: the position of the box (horizontal, vertical)z: monkey grasping the banana (1 or 0)

(w, x, y, z)

(w, x, y, z)(w, x, y, z)

monkey box

on top of the box

grasping the banana


Operator Difference (1)

(w, 0, y, z) (u, 0, y, z)goto(u)

(w, 0, w, z) (v, 0, v, z)pushbox(v)

precondition: x = 0

difference: The monkey is not at the location u.

precondition: w = y, x = 0

difference: The box is not at the location v.


Operator Difference (2)


difference: The monkey is not on the box.

precondition: x = y = C, x = 1, z = 0

difference: The monkey does not have bananas.

(w, 0, w, z) (w, 1, w, z)climbbox

(c, 1, c, 0) (c, 1, c, 1)grasp


Finding Key Operator (1)

(A, 0, B, 0) (C, 1, C, 1)

difference: The monkey does not have bananas.

(A, 0, B, 0) (C, 1, C, 1)(C, 1, C, 0)

difference: 1. The box is not at the location C. 2. The monkey is not at the location C. 3. The monkey is not on the box.

pushbox(C)goto(C)climbbox

P1

P2

grasp


Finding Key Operator (2)

(A, 0, B, 0) (C, 1, C, 1)(C, 1, C, 0)

difference: 1. The box is not at the location C. 2. The monkey is not at the location C. 3. The monkey is not on the box.

pushbox(C)goto(C)climbbox


(A, 0, B, 0)(B, 0, B, 0)

(B, 0, B, 0) (C, 0, C, 0) (C, 1, C, 0)

(C, 1, C, 1)

P11

P12

P13


References

[1] http://en.wikipedia.org/[2] 인공지능개론, 이광형, 조충호, 홍릉과학출판사, 2000

and/or graph search - wikimedia · 5a and/or graph 3 young won lim 14년 10월 27일 hanoi tower...

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