This preview shows pages 1–2. Sign up to view the full content.
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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 04/11/2010 for the course CSC CSC236 taught by Professor Farzanazadeh during the Spring '10 term at University of Toronto Toronto.
 Spring '10
 FarzanAzadeh

Click to edit the document details