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ARI711S - ARTIFICIAL INTELLIGENCE - 1ST OPP - JUNE 2022 |
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nAmlBIA unlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF COMPUTING AND INFORMATICS
DEPARTMENTOF COMPUTERSCIENCE
QUALIFICATION: BACHELOR OF COMPUTER SCIENCE
QUALIFICATION CODE: 07BACS
COURSE: ARTIFICIAL INTELLIGENCE
DATE: JUNE 2022
DURATION: 3 HOURS
LEVEL: 7
COURSE CODE: ARl711S
PAPER: THEORY
MARKS: 93
EXAMINER(S)
MODERATOR:
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
Prof. JOSE QUENUM
Mr STANTIN SIEBRITZ
INSTRUCTIONS
1. Answer ALL the questions.
2. Read all the questions carefully before answering.
3. Number the answers clearly
THIS QUESTION PAPER CONSISTS OF 3 PAGES
(Excluding this front page)
PERMISSIBLE MATERIALS
CALCULATOR
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ARl7115
Second Exam (continued)
July 2022
Question 1 ..................................................................
[25 points]
(a) Consider the blocks world. The blocks can be on a table or in a box. Consider three
[15]
generic actions: a0, a1, and a2 described as follows:
a0 : when applied to a block, will keep it in the box;
a1 : when applied to a block, will move it on the table;
a2: when applied to two blocks, will move the first one on top ofthe
second one.
Consider the following four states in the system:
S0 : all blocks are in the box, no block is on the table;
S1: only block Bis on the table; all other blocks are in the box;
S2: both blocks B and Care on the table, with Con top of B;
S3: blocks B, C and Dare on the table, with Don top of C and Con top of B.
Furthermore, additional information is provided in Table 1, where each state has a re-
ward, possible actions and a transition model for each action. Note that for a given ac-
tion, the probability values indicated in its transition model all sum up to 1.
Table 1: Additional information
State Reward Action
Transition Model
So
ro
aob
(1, So)
a1b
(Po,So); (Pi, S1)
r1
S1
aoc
(1, S1)
a1c (p5,S1);(pf,S4);(P½,S2)
a2c
(p5, S1); (Pi, S2);
r2
S2
aod
(l,S2)
a1d (p5,S2);(Pi,Ss);(p~,S3)
a2d
(P6,S2); (p1, S3);
S3
100
Assuming we model this problem as Markov Decision Process (MVP) and consider a
discount value CY, provide the utility of each of the states S0, S1 and S2 for the first three
iterations using the value iteration algorithm. Note that although the states S4 and S5
have not been defined, they should be assumed in the system.
(b) Consider the following policy, n0 = {So H aob,S1 H a1c, S2 H a2d}- Is n0 optimal?
[10]
Explain.
Question 2 ..................................................................
The diagram in Figure 1 represents the extensive form of a sequential game
[15 points]
1. Provide the strategic form associated with the game;
2. Does any player have a dominant strategy?
3. Is there a dominant strategy equilibrium?
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ARl711S
Second Exam (continued)
July 2022
2
4
1
0
1
0
2
3
Figure 1: Sequential Game
4. What are the Nash equilibria?
Question 3 ..................................................................
(a) Consider a game g whose strategic form is represented as follows:
Player2
[15 points]
[2]
Zo (7, 2) (2, 5) (6, 3)
Playerl
Jo (2, 2) (6, 5) (4, 8)
f 0 (3, 1) (2, 7) (4, 9)
Is there a dominated strategy for Player 2? If yes eliminate it;
(b) The resulting game is now called ()'. Is f 0 a worse strategy for Player 1 than playing a
[6]
mixed strategy of z0 and Jo in ()'?
(c) what is the payoff of each player when they play a mixed strategy with Player 1 eliminat-
[7]
ing f 0 in ()'?
Question 4 ..................................................................
[20 points]
Consider the blocks world. Here we have seven (7) blocks: A, B, C, D, E, F and G. There is also
a table with a capacity of three (3) blocks (i.e., three distinct blocks can lay on the table at
any point in time simultaneously). It is assumed that a block can either be inside the box or
outside. When outside the box, a block can either be on the table or on top of another block.
We have the following predicates:
ontable(x) : the block xis on the table;
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ARl711S
Second Exam (continued)
July 2022
on(x, y) : the block x lays on top of the blocky;
clear(x) : the block xis clear, i.e., there is nothing on top of it;
inbox(x) : the block xis inside the box.
Moreover, the following actions are introduced:
pick(x) : which picks a block from the box and drops it on the table;
drop(x, y) : which drops the block on either the table or another block.
Consider a partial plan Q containing two actions: a0 and a21 with a0 --<at. The action a0 has
the following effect:
ontable(B); ontable(C);ontable(E);clear(B); clear(C);clear(E);inbox(D);inbox(F);inbox(G);
The action at leads to a goal state and has the following pre conditions:
ontable(F);ontable(A); clear(Table); on(B, A); on(C, B); on(D, C); on(E, F);
Modify Q to generate a complete and correct plan.
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End of Exam