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CS 540-1: Introduction to Artificial Intelligence
Exam 2: 11am-12:15pm, November 21, 1994
CLOSED BOOK
(one page of notes allowed)
Write your answers on these pages and show your work. If you feel that a question is not fully specified, state any assumptions you need to make in order to solve the problem. You may use the backs of these sheets for scratch work.
Write your name on this and all other pages of this exam. Make sure your exam contains six problems on six pages.
Name ________________________________________________
Student ID ________________________________________________
Problem Score Max Score
1 _____ 30
2 _____ 22
3 _____ 18
4 _____ 12
5 _____ 6
6 _____ 12
Total _____ 100
PROBLEM 1 - Search (30 points)
Consider the search graph drawn below; the start and goal states are labeled. Note that arcs are directed. For each of the search strategies listed below, indicate which goal state is reached (if any) and list, in order, the states expanded. (A state is expanded when it is removed from the OPEN list.) When all else is equal, nodes should be expanded in alphabetical order.
Start
A B
C D
E
Goal
Goal
1
1 4
1
5
7 3
2
6
10
11
3 2
7
KEY
cost of traversing this arc is X
estimated cost to nearest 15 goal is Y
14
13 11
4
0
0
3
21
Y
X
14 F
Depth-First Search
Goal state reached: _____ States expanded: ____________________________________
Iterative Deepening
Goal state reached: _____ States expanded: ____________________________________
Best-First Search (using f=g+h )
Goal state reached: _____ States expanded: ____________________________________
Hill Climbing (using the h function only)
Goal state reached: _____ States expanded: ____________________________________
Beam Search (with a beam width of 2)
Goal state reached: _____ States expanded: ____________________________________
Would the h function in this graph lead to an admissible search? ______
Explain your answer:
PROBLEM 3 - Backward-Chaining: Prolog (18 points)
a) Consider the following Prolog rulebase:
p(1,2). p(3,3). p(2,1). q(1,2). q(2,1). q(2,2). q(3,3). r(2,1). r(2,2). s(X1,Y1) :- p(X1,Y1), q(Y1,X1), r(X1,X1). s(X2,Y2). r(X3,Y3) :- q(X3,Y3). w(X4,Y4) :- p(X4,Y4), q(2,Z4), r(X4,Z4).
For the following queries, report the answers that Prolog a requested answer. Report fail is Prolog would not be able to find a requested answer.
i) ?- s(2,1). First Binding List Found: _____________________________
Second Binding List (if one): _____________________________
Third Binding List (if one): _____________________________
ii) ?- w(U,V). First Binding List Found: _____________________________
Second Binding List (if one): _____________________________
Third Binding List (if one): _____________________________
b) Write a Prolog program for sisters(X,Y) , which determines if X and Y are sisters. You may only assume that the predicates grand_parent(X,Y) , parent(X,Y) , ancestor(X,Y) , male(X) , female(X) , tall(X) , young(X) , older_than(X,Y) , and different(X,Y) are defined. Different(X,Y) is true when X and Y have been bound to different constants; the semantics of the other predicates should be obvious (the binary ones, predicate(X,Y) , can be read ‘‘ X is a predicate of Y ’’).
PROBLEM 4 - Important AI Concepts (12 points)
In the space below, provide brief and succinct summaries of the importance of the following AI concepts.
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horizon effect
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interacting subgoals
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negation-by-failure
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PROBLEM 5 - Game Playing (6 points)
Assume that a game has a static-board evaluator (SBE) that only returns one of three values: -1 (lose), 0 (draw), and 1 (win). Consider the game tree drawn below. What is the fewest possible number of calls to the SBE? To illustrate your answer, label those leaf nodes that would have to be called with the score that the SBE would have to return. (If you feel there are several way that the fewest calls could occur, you need only show one of them.)
maximizer
minimizer
maximizer
