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ECS 120: Introduction to Theory of Computation
Homework 3
Problem 1.
Suppose that
L
is DFAacceptable. Show that the following languages are
DFAacceptable, too.
Part A.
Max
(
L
) =
{
x
∈
L
: there does not exist a
y
∈
Σ
+
for which
xy
∈
L
}
.
Part B.
Echo
(
L
) =
{
a
1
a
1
a
2
a
2
···
a
n
a
n
∈
Σ
*
:
a
1
a
2
···
a
n
∈
L
}
.
Problem 2.
Prove that the NFAacceptable languages are closed under reversal.
Problem 3.
Exhibit decision procedures (algorithms) which answer the following ques
tions.
(a)
Given a DFA
M
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Unformatted text preview: , does L ( M ) contain a string of the form ( babb ∪ aa * b ) * ? (b) Given NFAs M 1 and M 2 , is  L ( M 1 )  =  L ( M 2 )  < ∞ ? (c) L = {h α i : α is a shortest regular expression whose language is L ( α ) } . Problem 4. Transform the following NFA into a DFA accepting the same language. Bonus (Challenging). If L is a language over the unary alphabet { a } , then L * ∈ Reg . 1...
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This note was uploaded on 04/29/2010 for the course ECS 222 taught by Professor Mr. during the Spring '10 term at UC Davis.
 Spring '10
 mr.

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