Midterm Exam Sample. Time: 150 minutes - Computer Science

91.502 Foundations of Computer Science 1
Midterm Exam Sample. Time: 150 minutes
This sample only gives you an idea of the difficulty level of the exam and topic coverage.
Problems in the actual exams will be similar to what you have seen in the lectures and the
textbook and what you have done in your homework assignments.
The exam is closed book and contains five problems. Complete as many problems as you can,
show your work, and justify your answers. Keep your answers clean and don’t include
anything that is irrelevant. You will be graded not only on the correctness of your answer,
but also on the clarity you express it.
Problem Points Grade
1 20
2 20
3 20
4 20
5 20
Total 100
I have abided by the Academic Honor Code on this exam.
Signature:
Date:
Name (please print):
UMass Lowell
Midterm Exam Sample

91.502 Foundations of Computer Science 2
1. (20 points) Use the technique of product automata to show that the intersection of a
regular language and a context-free language is context-free.
2. Consider ɛ-NFA M 0 = (Q, {0, 1}, δ, q 0 , F ) given below:
δ ɛ 0 1
→ A {B, E} ∅ ∅
B ∅ ∅ C
∗C ∅ C C
E ∅ {E, F } E
∗F ∅ ∅ ∅
(a) (5 points) Convert M 0 to an equivalent DFA M 1 .
(b) (5 points) Minimize M 1 to an equivalent DFA M 2 .
(c) (5 points) Derive a regular expression for L(M 0 ) from M 2 .
(d) (5 points) Construct a right-linear grammar from M 2 that generates L(M 0 ).
3. Let L = {xx | x ∈ {0, 1} ∗ }.
(a) (10 points) Show that L is not regular without using the Pumping Lemma.
(b) (10 points) Show that L is not regular using the Pumping Lemma.
4. (20 points) Show that context-free languages are not closed under intersection.
5. (20 points) Show that a one-tape Turing machine can be simulated by a Pushdown
Automaton with two (unbounded) stack memories.
UMass Lowell
Midterm Exam Sample