Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

CS402 Automata Assignment 04 Solution fall 2012

VIEWS: 1,179 PAGES: 4

CS402 Automata Assignment 04 Solution fall 2012

More Info
									   Come & Join Us at VUSTUDENTS.net

  For Assignment Solution, GDB, Online Quizzes, Helping Study material,
   Past Solved Papers, Solved MCQs, Current Papers, E-Books & more.




 Go to http://www.vustudents.net and click Sing up to register.




VUSTUENTS.NET is a community formed to overcome the disadvantages of distant
learning and virtual environment, where pupils don’t have any formal contact with their
mentors, This community provides its members with the solution to current as well as the
past Assignments, Quizzes, GDBs, and Papers. This community also facilitates its
members in resolving the issues regarding subject and university matters, by providing
text e-books, notes, and helpful conversations in chat room as well as study groups. Only
members are privileged with the right to access all the material, so if you are not a
member yet, kindly SIGN UP to get access to the resources of VUSTUDENTS.NET

» » Regards » »
VUSTUDENTS.NET TEAM.
Virtual University of Pakistan




             Come and Join Us at www.vustudents.ning.com
       CS402_4RTH ASSIGNMENT IDEA SOLUTION
Answer # 1 (a):
                            Pumping Lemma Version I
Let us suppose a word that belongs to given language like as
W = aaabbbbbb
Where
x =aa
y = abbbb
z bb

 xyyz Contain many number of         and many numbers of       but this string will not
belong to L because the substring ab can occur at the most once in the words of L, while
the string xyyz contains the substring ab twice. On the other hand if y-part consisting of
only       or     then xyyz will contain number of       different from number of
this shows that pumping lemma does not hold and hence the language is not regular.

                            Pumping Lemma Version 2
To prove this language to be non regular, suppose contrary, i.e. FACTORIAL is a regular
language, then there exist an FA accepts the language FACTORIA. Let the number of
states of this machine be 345 and choose a word w from FACTORIA with length more
than 345, say, 347 i.e. the word w = a347.Since this language is supposed to be regular,
therefore according to pumping lemma xynz                                             L.
Consider n=348, then xynz = xy348z = xy347yz. Since x, y and z consist of          , so the
order of x, y, z does not matter i.e. xy347yz = xyzy347 = a347 y347, y being non-null
string and consisting of      it can be written y = am, m= 1, 2,3, , 345 . Thus xy348z =
a347 (am) 347 = a 347(m+1) Now the number 347(m+1) will not remain FACTORIA for
m = 1, 2,3, , 345 . That shows that the string xy348z is not in FACTORIA. Hence
pumping lemma version II is not satisfied by the language FACTORIAL. Thus
FACTORIAL is no regular.

Answer # 1 (b):
According to PUMPING LEMMA I AND II given language is not regular explained as
above.




              Come and Join Us at www.vustudents.ning.com
         ((a+b)(a+b))* = (aa + ab + ba + bb)* given below

S    XY
X     aX bX
Y    aY bY

                               Odd Length Language


CFG for ((a+b)(a+b))* (a+b) = (aa + ab + ba + bb)* (a+b) given below

S    BaB | AbA | X | Y
B    bbB | /\
A    aaA | /\
X    BbabB
Y    AabaA
S    XY XX
Y    aY bY
X    aaa aba bab bbb

Answer # 2 (b):
                        Even Multiple of Three Palindrome
S    Y|Z|YZ|ZY
Y    b| a Y a | a Y b | b Y a | bY b
Z    a|aZa|aZb|bZa|bZb

                        Odd Multiple of Three Palindrome
S    Y|Z|YZ|ZY
Y    b| a Y b | b Y a
Z    a | a Z b | bZ a




                Come and Join Us at www.vustudents.ning.com
S    aAA bBB
A    bB Z
B    aA

Her we can see that B also has null production so B is null production A & S are said to
be Null able production.
S aAA aA a bBB bB b
A    bB Z b
B    aA a

Answer # 3 (b):
S    aAA bBB
A    bB Z
B    aA
Z

Her we can see that B & Z & S also have null production so B & Z & S are null
production. A is said to be Null able production.

S    aAA aA a bBB bB b
A     bB Z b
B    aA a
Z    a b




              Come and Join Us at www.vustudents.ning.com

								
To top