CSC236H: Introduction to the Theory of Computatoin
Homework 4
Due on Tuesday March 16, 2010
1. Consider the following DFA. Solid edges have label
a
and dashed edges have label
b
.
Problem 3
Consider the following DFA. Solid edges have label
a
and dashed edges have label
b
.
1
4
7
2
5
8
3
6
9
(a) Describe in one sentence what the language of this DFA is.
(b) Give the smallest equivalent DFA to this DFA.
3
(a) Describe in one sentence what the language of this DFA.
(b) Give a DFA equivalent to this DFA with only three states.
(c) Prove that your DFA is correct, i.e. its language is the same as what you have described in (a).
2. Let
L
=
{
w

w
contains an equal number of occurrences of the substrings 01 and 10
}
.
This means
that 101
∈
L
because 101 contains a single occurrence of 01 and a single occurrence of 10.
On the
other hand, 1010
6∈
L
as it has two 10s and one 01.
•
Construct a DFA that recognizes
L
.
•
Justify your answer by giving a formal description of the set of strings that each state characterizes.
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 Spring '10
 FarzanAzadeh
 Regular expression, Regular language, M3 Halftrack, M2 Browning machine gun, Theory of Computatoin

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