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CS381
Final Exam
Thursday Dec 19, 2002
Fall 2002
Location
Olin 155
12:002:30pm
This is a 2 and ½ hour in class closed book exam.
All questions are straightforward and
you should have no trouble doing them.
Please show all work and write legibly.
Thank
you.
1.
Let
*
)
(
b
a
R
+
⊆
be a regular set.
Consider the set consisting of all strings that can be
obtained from strings in R by deleting two b’s.
Is this set regular?
Give rigorous proof
of your answer.
2.
Let
*
)
(
c
b
a
R
+
+
⊆
be a regular set.
Rearrange the symbols in each string of R so
that all
a
’s appear first, then the
b
’s and then the
c
’s.
a) Is the resulting set regular?
b) Is it context free?
3. Prove or disprove that
{ }
l
j
or
k
i
either
d
c
b
a
l
k
j
i
=
=

is a contextfree language.
4.
Prove or disprove each of the following:
a) The class of contextfree languages is closed under intersection.
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 Fall '07
 HOPCROFT

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