Download 22C:145 ARTIFICIAL INTELLIGENCE Midterm Exam, March 2013

22C:145 ARTIFICIAL INTELLIGENCE
Midterm Exam, March 2013
Open book and notes; no digital devices
Total points = 100
1. (30 points) Suppose a search problem is represented by the following graph:
where the cost of each edge is given, A is the start node and F is the goal. The heurist
function is given as follows:
n
h(n)
A
14
B
8
C
1
D
12
E
6
F
0
G
1
H
3
Assuming the neighbors of a node are explored in the alphabeta order of their names,
please list the nodes entering the Closed list as the search goes on using the following
strategies, respectively, and list the path found from A to F .
• Depth-first search
• Uniform-cost search: f (n) = g(n), the total cost of n from the start node.
• A∗ : f (n) = g(n) + h(n)
Answer keys:
• Depth-first search: the open list is a stack (last-in first-out)
open
A
CD
CBEH
CBEF
CBE
closed
A
AD
ADH
ADHF
The path is A, D, H, F .
• Uniform-cost search: f (n) = g(n), the total cost of n from the start node.
The open list is a priority queue.
open
A
C5, D2
C5, B6, E5, H9
B6, E5, H9, G9
B6, H7, G9
H7, G9, F 14
G9, F 13
F 13
closed
A
AD
ADC
ADCE
ADCEB
ADCEBH
ADCEBHG
ADCEBHGF
The path is A, D, E, H, F .
• A∗ : f (n) = g(n) + h(n) The open list is a priority queue.
open
A
C6, D14
D14, G10
D14, E20
E11, B14, H12
B14, H10
B14, F 13
B14
The path is A, D, E, H, F .
closed
A
AC
ACG
ACGD
ACGDE
ACGDEH
ACGDEHF
2. (30 points) You are asked to solve the
following initial configuation:
5-queen puzzle using the local search with the
∗
∗
∗
∗
∗
The evaluation function is the number of pairs of attacking queens (10 for this initial configuration). A neighbor of a configuration is defined as changing the position of a queen
in one row to its neighboring (left or right) positions (so for 5-queen, there are at most 10
neighbors). Please show what is the best neighbor (pick one if there are more than one)
in each move. The search stops when either you found a model or you reached a local
optimum.
Answer keys:
The numbers in the following table indicate the number of conflicts when the queen in that
row moves to its position:
∗
7
7
∗
7
7
∗
7
7
∗
7
7
∗
So any move will be equally good. Let us pick the first queen to move and recompute the
number of conflicts:
10
4
∗
∗
5
7
5
∗
5
6
∗
5
5
∗
The best move will be for the second queen to move left. We reach a local minimum as
shown below: no moves reduce the number of conflicts below 4.
7
∗
∗
7
4
4
∗
4
4
∗
4
4
∗
3. (40 points) Please first express the following statements in First-order logic with quantifiers
(no free variables), and then in clauses along with a resolution proof that Marcus hates
Caesar. Finally, write clauses in Prolog format and provide the query that Marcus hates
Caesar.
Marcus is a Pompeian. All Pompeians are Romans. Caesar is a ruler.
All Romans are either loyal to Caesar or hate Caesar. People only try
to assassinate rulers they are not loyal to. Macus trys to assasinate
Caesar.
Answer keys: For first-order formulas, clauses, and the resolution proof, please consult
http://www-rci.rutgers.edu/∼cfs/472 html/Logic KR/resolution.html
The Prolog program is given below:
pompeian(marcus).
roman(X) :- pompeian(X).
ruler(caesar).
hate(X, caesar) :- roman(X), notLoyalto(X,caesar).
notLoyalto(X, Y) :- tryassasinate(X,Y), ruler(Y).
tryassasinate(marcus, caesar).
The Prolog query is
?- hate(marcus, caesar).