And or search in AI

1. AND-OR search
With Example
15

2. AND-OR Search (AO*)
 AND/OR graph is a form of graph or tree
used in problem solving and problem
decomposition. The nodes of
the graph represent states or goals and their
successors are labeled as either AND or OR
branches.
 The AND successors are subgoals that must
all be achieved to satisfy the parent goal,
while OR branches indicate alternative
subgoals, any one of which could satisfy the
parent goal.
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Goal: Acquired Mobile
Goal:
Buy a
Mobile
Goal:
Earn
some
money
Goal:
Steal
Mobile

3. Subscribe
A
D
C
B
1
1
1
6 5
3
AND
OR
f(n)=g(n)+h(n)
f(n)=cost function
g(n)= Actual cost or edge value.
h(n)= heuristic value
Path-1 (AB) 1+6=7
Path-2 (ACD) 1+3+1+5=10
7 10
AB

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A
B D
C
F
E H
G J
I
1
1
1
1
1
1 1 1 1
15 8 7 1 6 3
10
13
20
f(n)=g(n)+h(n)
Path1: f(AB)=1+20=21
Path2: f(ACD)=1+13+1+10=25
f(BEF)= 1+15+1+8= 25
f(AB)=1+25=26 (revised)
f(DIJ)=1+6+1+3= 11
f(CGH)= 1+7+1+1=10
f(ACD)= 1+10+1+11=23 (revised)
25
min(26,23)=23
11
10
21 25
26 23

5. Difference between A* and AO*
A* algorithm
 A* algorithm is OR graph
algorithm.
 It just find only one solution.
 A* algorithm guarantees to give
an optimal solution.
AO* algorithm
 AO* is a AND-OR graph algorithm.
 It find more than one solution by
ANDing two or more branches.
 AO* algorithm does not always give
optimum solution. AO* doesn't
explore all other solutions once it got
a solution.
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6. Thanks For
Watching
Reference:
Artificial Intelligence
A Modern Approach Third Edition
Peter Norvig and Stuart J. Russell
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