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Spring 10: CSci 4011—Formal Languages and Automata Theory
40 points
Homework 5
Out Fri., 2/26
Due Fri., 3/05
Please review the instructions given with Homework 1, as they apply to this home
work, too.
Please hand in your answers to the following.
Note:
All Exercise/Problem/Theorem/etc. numbers correspond to the
U.S. 2nd edition
of the
Sipser text. If you have the International edition, please check that the numbers match the ones in
the U.S. edition.
1.
Let
A
=
{
0
n
1
n

n
≥
0
}
. Give a CFG for
¯
A
, the
complement
of
A
.
Hint:
First express
¯
A
as the union of three “simpler” languages.
2.
Let
A
=
{
w
∈ {
0
,
1
}
*

w
 ≥
3 and the third symbol of
w
is 0
.
}
.
A
is regular. Give a CFG for
A
by constructing a DFA for
A
and converting the DFA to a CFG. (For your satisfaction, verify your
answer by running a few strings that are in/not in
A
through your DFA and by generating/failing
to generate these strings in the constructed CFG. Do not turn this part in.)
3.
Convert the CFG below to Chomsky Normal Form using the procedure outlined in the proof of
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 Spring '08
 NADATHUR

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