CS 154
Intro. to Automata and Complexity Theory
Handout 14
Autumn 2006
David Dill
October 24, 2006
Problem Set 4
Due: October 31, 2006
Homework:
(Total 100 points) Do the following exercises.
Problem 1.
[20 points]
Consider the DFA given by the following transition table.
0
1
→
A
B
J
B
H
C
*
C
D
G
D
E
C
*
E
F
G
F
C
E
*
G
J
C
H
B
G
I
H
E
J
H
A
Give the minimum equivalent DFA. For each state of the minimized DFA, specify the set of equiv
alent states of the original DFA.
Problem 2.
[15 points]
Consider the (deterministic) Turing machine
M
given by
M
= (
{
q
0
, q
1
, q
2
}
,
{
a, b
}
,
{
a, b, B
}
, δ, q
0
, B,
{
q
2
}
)
which has exactly four transitions defined in it, as described below.
1.
δ
(
q
0
, a
) = (
q
0
, B, R
)
2.
δ
(
q
0
, b
) = (
q
1
, B, R
)
3.
δ
(
q
1
, b
) = (
q
1
, B, R
)
4.
δ
(
q
1
, B
) = (
q
2
, B, R
)
(a).
[5 points]
Specify the execution trace of
M
on the input string
abb
.
(b).
[5 points]
Provide a regular expression for the language of this Turing machine.
(c).
[5 points]
Suppose that we add the following transition to the above machine.
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 Winter '08
 Motwani,R
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