# ECE 457 Applied Artificial Intelligence Midterm Examination

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"ECE 457 Applied Artificial Intelligence Midterm Examination"

```					                                     E&CE 457

Applied Artificial Intelligence

Midterm Examination

Summer 2001

June 15, 2001

Instructor

Kostas Kontogiannis

Notes:
Closed book exam
No calculators allowed
This exam has 3 pages
Questions worth 70 marks
If it seems that there is information missing state your assumptions and proceed with your
Question 1. [12 Marks]

•     Provide the definitions for the following concepts: i) entailment, ii) inference, iii) model,
iv) satisfiability, v) soundness of an inference method, vi) completeness of an inference
method [9 marks]
•     How entailment and inference relate? [3 marks].

Question 2. [10 Marks]

1. Prove by resolution that the following sentence is non-satisfiable:

•     (A v (B t C)) ∧ (A v B) ∧ (A v ¥ C) ∧ (C v A) [5 marks]

2. Prove using resolution refutation that from the following sentence
• ¥A ∧ (C t A) ∧ (B t (A - C))

you can deduce (¥A ∧ ¥B ∧ ¥C) [5 marks]

Question 3. [20 marks]

Consider the six-tile puzzle problem. A tile can be moved up, down, left, right, only if the spot
adjacent to it is empty. In Fig.1 the move of a tile labeled with the number (7) is moved to the
left.

•     Model the problem efficiently as a sequence of states and operations Up, Down, Left,
Right. [9 marks]
•     Develop meaningful cost and heuristic estimate values for the model and trace the A*
algorithm on the generated search space. The initial and the goal states are respectively:

Initial-State                Goal State
7 X 1                         7 2 1
3 2      8                    3 8 X

7 X 1
3 2      8

Figure 1. Moving tile 7 to the left. The X denotes an empty spot.

X 7 1
3    2 8
Question 4. [18 marks]

Consider the following tree:

A1                           MAX Level

A2              A3                      A4   MIN Level

MAX Level
A5    A6 A7 A8 A9 A10 A11 A12 A13
Value:     3     13 8   6 2   4 2 5       8

•   Trace and explain the ALPHA-BETA procedure as applied to the above game tree.[9
marks]
•   Provide the time and space complexity and whether they are optimal and complete the
following algorithms. Assume a branching factor b, the depth of the solution d, and a
maximum depth of the search tree m.[5 marks]
o Depth limited (depth limit is l)
o Iterative Deepening
o Hill Climbing
o A*
•   Provide the proof that A* is optimal.[4 marks]

Question 5. [10 marks]

A           4:3    B         5:3   C

1:4
S                   5:3              5:2                     G
3:0.5
3:3
D         2:2 E       4:1 F

Consider the above graph consisting of nodes S, A, B, C, D, E, F, and G. Each arc between nodes
N1 and N2 in the graph is labeled by two numbers w1 and w2 using the format w1:w2 meaning
that the cost from N1 to N2 is w1 and an underestimate from N1 to the goal is w2.
Trace the following algorithms for solving the problem of going from node S to node G:
• Best First [5 marks]
• Beam Search for n=2 [5 marks]

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