DOEACC Society 2006 DOEACC B Level BE2 AI and Applications ( ) - Question Paper
Friday, 14 June 2013 07:50Web
BE2-R3: ARTIFICIAL INTELLIGENCE AND APPLICATIONS
NOTE:
Time: three Hours Total Marks: 100
1.
a) Suppose h1(x, y) and h2 (x, y) are 2 heuristic functions constructed for use in the water jug
problem. x and y denote the contents of the 4L and 3L jugs respectively. provided h1(x, y)>
h2(x, y) for all x, y. Which of the 2 heuristic functions should we use and why?
b) provided the subsequent 2 propositional statements, obtain the interpretation(s), which satisfy
these statements.
(p ® q) ® p
and (q ® p) ®q
c) provided P (B/ A) = 0.7, P (A ÇB) = 0.2, P (A ÇØB)= 0.4 and P (B)= 0.9, obtain P(A/ B).
d) Draw CD representation of the subsequent sentence: “Smoking is harmful to health.”
e) Let S={(1,3), (2,5), (3,4), (9,22), (4,16)} be a set of co-ordination of five points and y=2x+3
be a linear classifier of the region. Determine the 2 classes.
f) Determine the minimal number of colors needed to color the subsequent map.
g) provided mA(x)={20/ 0.2, 30/0.4, 40/ 0.6} and mB (x) = {20/ 0.4, 30/0.6, 40/ 0.2}, obtain mAÇB (x).
(7´4)
2. Consider 8-puzzle problem:
a) State the rules you need to use to solve the above issue.
b) Suggest two heuristic functions to handle the issue using A* algorithm.
c) Consider a starting state and a goal state. Expand the starting state using A* algorithm.
Use any 1 heuristic function you considered in part b) above.
(4+4+10)
3.
a) provided the query Query : ¬ Taxpayer (X), draw the SLD tree for the subsequent logic
program. Show back-tracking on the diagram.
1. Taxpayer (X) ¬ Foreigner (X), cut, fail.
2. Taxpayer (X) ¬ Spouse (X, Y), Annual-Inc (Y, Earning), Earnings > 40,000, cut
fail.
3. Taxpayer (X) ¬ Annual-Inc (X, Earning), 30,000 < Earnings, 50,000 > Earnings.
4. Foreigner (ram) ¬
BE2-R3 Page one of three January, 2006
A3
A2 A4 A6
A1 A5
1. ans ques. one and any 4 ques. from two to 7.
2. Parts of the identical ques. should be answered together and in the identical
sequence.
5. Spouse (ram, mita) ¬
6. Annual-Inc (mita, Earnings) ¬
7. Earnings = 45,000 ¬
8. Annual-Inc (Lakshman, 35,000) ¬
b) State the most general unifier:
W = {P (a, x, f (g(y))), P(z, f(z), f(u)))}
c) describe soundness and completeness of propositional logic using Axiomatic System.
(12+3+3)
4.
a) Write grammar rules, which can handle the subsequent sentence and also generate the
parse tree
‘A barking dog seldom bites.’
b) Draw the semantic network for the subsequent sentence.
Every town dog has bitten the watchman.
(9+9)
5.
a) In a blocks world planning problem, provided the state: On (A, B), On (B, Table), On (C,
Table), Clear (A) and Clear (C), and the goal state: On (B, A), On (C, B), On (A, Table)
and Clear (C), where On (X, Y) means the object X is on object Y and clear (X) means
there is nothing on top of object X. The operators in the current situation are provided by the
subsequent if-add-delete rules.
Rule 1: If On (X, Y), Clear (X), Clear (Z)
Then Add-List: On (X, Z), Clear (Y),
and Delete-List: On (X, Y), Clear (X).
Rule 2: If On (X, Y), Clear (X)
Then Add-List: On (X, Table), Clear (Y),
and Delete-List: On (X, Y).
Rule 3: If On (X, Table), Clear (X), Clear (Z)
Then Add-List: On (X, Z),
and Delete-List: Clear (Z), On (X, Table).
Design a plan by forward/backward reasoning on the state-space.
b) Consider a issue with a constraint set which exhibits a partial satisfaction w.r.t
primitive constraints but total satisfiability is not feasible. The issue is: provided the
constraint C=(x
(9+9)
6.
a) Show that
P(X | E)
P(Y| X,E) = P(X | Y,E).P(Y | E)
BE2-R3 Page two of three January, 2006
b) Consider a temporal world describing the seasons in a year. Probability that “now it is
winter” is denoted by p (winter). Thus for four seasons suppose we are provided that,
P (winter) =1/4
P (summer) ½
P (spring) 1/8
P (rainy season)= 1/8
Let s be a fact denoting that “it is very cold today.” provided that
P (s/ winter) = 0.2
P (s/ rainy season) = 0.6
P (s/ summer) = 0.1
P (s/ spring) = 0.1
Determine the probability that the statement s is actual.
(9+9)
7.
a) Let
X1 = [ one –1 one ]
X2 = [ -1 one –1 ]
and X3 = [ -1 –1 one ]
be 3 such stable states in a discrete Hopfield net. Encode the weight matrix W for
such system, and hence check that X1 is a stable state.
b) Design a perceptron classifier that classifies a 2D space into 2 regions using the
inequality: 3x1 + 4x2 £12.
(9+9)
BE2-R3 Page three of three January, 2006
| Earning: Approval pending. |
