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Handout #60
CS103
June 2, 2010
Robert Plummer
Problem Set #8 Solutions
All problems are from Sipser.
1. Exercise 4.2, p. 183.
EQ
DFA,REX
= {
A, R
 A a DFA, R a regular expression and L(A) = L(R)}
The following TM E decides EQ
DFA,REX
:
E = "On input
A, R
:
1. Convert regular expression R to an equivalent DFA B using the procedure
given in Theorem 1.54.
2. Use the TM F for deciding EQ
DFA
given in Theorem 4.5 on input
A, B
.
3. If
F accepts,
accept
.
If F rejects,
reject
."
2. Problem 4.12, p. 183.
Note that L(R)
L(S) if and only if L(S)
L(R) =
.
The following TM decides A:
X = "On input
R, S
where R and S are regular expressions:
1. Construct DFA E such that L(E) = L(S)
L(R).
2. Run TM T for deciding E
DFA
from Theorem 4.4 on
E
.
3. If T accepts,
accept
.
If T rejects,
reject
."
3. Problem 4.15, p. 184.
The following TM X decides A:
X = "On input
R
where R is a regular expression:
1. Construct DFA E that accepts
*111
*.
2. Construct DFA B such that L(B) = L(R)
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This document was uploaded on 02/08/2011.
 Fall '09

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