CS 373 – Fall 2003  NMG
****** SOLUTION****post****
September 27, 2003
Homework Assignment 4 for chapter 4, PROB 9 DROPPED
Due Friday, 10/3/03 After class
Problems related to chapter 4:
General directions:
1. Clearly justify all statements in your proofs
2. If using a counter example to disprove, give a SPECIFIC example
3. For pumping lemma questions,
Use the text book format of a r game against an opponentr and all steps must be
explained.
EXPLICITLY SPECIFY:
a.
Pumping lemma integer m which starts off the proof.
Although you cannot
assume a specific value for the integer, show how your knowledge of its existence
is used.
“m”, must be explicitly shown in your formulas for the pumped string.
b.
One specific string which you choose
c.
Form of the partition "the opponent is capable of choosing" as a result of your
string choice.
d.
A value of i which you will use to pump up/down.
P1. (10 points)
Prove or disprove: If L
1
and L
2
are nonregular languages, then
L
1
∪
L
2
is non
regular.
P2 . (10 points)
Show that if L
1
and L
2
are languages over {a, b} where L
1
is regular and L
2
is
nonregular, then L
1
∪
L
2
may be either regular or nonregular, depending on L
1
and L
2
.
P3.
(15 points total )
Drill Time!.
Use the pumping lemma for regular languages to show that
the following languages are not regular (assume
∑
contains he symbols used in the definitions of
the languages):
a.
(5 points)
L = {a
3i
b
i
: i
≥
1}
… a warmup exercise!
b.
(5 points)
L = (a
n
b
m
: n > m }
c.
(5 points)
Show that L = {a
g
b
h
c
h
: g > 0 and h > 0 .
P4
.
(10 points)
Prove that the language:
L = { a
n
b
j
: n/j is an integer, and n
≥
0, j > 0 }
is not regular.
P5 . (10 points)
Use the pumping lemma for regular languages to show that the language below
is not regular.
L = {a
n^3
: n > 0 }
where n^3
means n
3
(problem doing double superscript).
Hint:
Consider the binomial expansion of (m+1)
3
.
P6.
(10 points)
Find a
regular
language which is a proper subset of the language:
L = {a
n
b
n
: n
≥
0}.
CS 373
Fall 2003
Solution key
page 1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
P7. (15 points)
Without using the pumping lemma prove that L = {a
n
b
m
: n
≥
m} is not regular.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Icamarra
 Regular expression, Regular language, Lemma, L1 L2

Click to edit the document details