CS402 Theory of Automata Mid Term Examination – Spring 2011 virtual university of pak

[Vuhelper]

CS402 Theory of Automata
Mid Term Examination – Spring 2006
Time Allowed: 90 Minutes
Please read the following instructions carefully before attempting any
question:
1. This examination is closed book, closed notes, closed
neighbors.
2. Answer all questions.
a. There is no choice.
b. You will have to answer correctly all questions in this
examination to get the maximum possible marks.
3. Do not ask any questions about the contents of this
examination from anyone.
a. If you think that there is something wrong with any of the
questions, attempt it to the best of your understanding.
b. If you believe that some essential piece of information is
missing, make an appropriate assumption and use it to
solve the problem.
4. You are allowed to use any Software for Diagrams and Symbols
like MS Word, MathType and Visio etc.
**WARNING: Please note that Virtual University takes serious note of
unfair means. Anyone found involved in cheating will get an `F` grade in
this course.
Question No. 1 Marks : 1
If s=abcd is a string defined over Σ = {a,bc,d} then reverse of s is dcba.
􀂐 True
􀂐 False
Question No. 2 Marks : 10
Find the regular expression associated to the following FA. Show all steps.
[Hint: use FA to GTG and GTG to RE.]
Question No. 3 Marks : 1
Σ
= {aa, b}, length(aaaabaabb) = 5.
􀂐 True
􀂐 False
Question No. 4 Marks : 1
Every NFA can be converted into FA.
􀂐 True
􀂐 False
Question No. 5 Marks : 1
There can be more than one start states in TG.
􀂐 True
􀂐 False
Question No. 6 Marks : 1
A regular language can not be infinite.
􀂐 True
􀂐 False
Question No. 7 Marks : 10
a) Write the recursive definition of the following language. [6]
L = Defining the language {a2n b4n }, n=1,2,3,… , of strings defined over Σ={a, b}
b) Write a regular expression of the language having strings that either start or end with
“00” and have no more zeroes. Where the alphabet is {0, 1}. [4]
Question No. 8 Marks : 1
Kleene star of {1} generates {1, 11, 111, 1111, 11111 ……}.
􀂐 True
􀂐 False
Question No. 9 Marks : 10
a) Define NFA-null. [4]
b) Draw DFA for the following NFA. [6]
Question No. 10 Marks : 1
If a regular language is empty then we denote it like L = Ǿ (fi).
􀂐 True
􀂐 False
Question No. 11 Marks : 1
Recursive method for defining language is only for regular languages.
􀂐 True
􀂐 False
Question No. 12 Marks : 1
aa* = a+ ?
􀂐 True
􀂐 False
Question No. 13 Marks : 1
The language equal means number of a’s and b’s are equal with null string.
􀂐 True
􀂐 False