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Comprehensive Exam: Autumn
200001
Automat
a
and Formal Languages
(60
points)
Problem
1.
[lo points]
Consider the language
L
defined by the regular expression 00'10. Provide a PDA
M for this
language using as few states as possible. Note that there is a PDA with only
1 state and
that the number of points you get will depend on the number of states used in your solution.
Problem
2.
[18 points]
Decide whether the following statements are TRUE or FALSE. You will receive
3
points for
each correct answer and
2 points for each incorrect answer.
1. If
L1
and
L2
are both nonregular, then
L1
n
L2
must be nonregular.
2.
L
=
{w E
{a,
b, c)'
(
w does not contain an equal number of occurrences of a, 6, and c)
is contextfree.
3.
Let
L
represent the language of a nondeterministic finitestate automaton
N; then,
swapping the final and nonfinal states of
N gives a machine
N' whose language is the
complement of
L.
4. Assume that
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 '08
 Motwani,R

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