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Tuesday, November 6, 2012

AUTOMATA THEORY SOLVED MCQS


AUTOMATA THEORY MCQS

(1) For a given input, it provides the compliment of Boolean AND output.

NAND box (NOT AND)
DELAY box
OR box
AND box

(2) It delays the transmission of signal along the wire by one step (clock pulse).

NAND box (NOT AND)
DELAY box
OR box
AND box

(3) For the given input, it provides the Boolean OR output

NAND box (NOT AND)
DELAY box
OR box
AND box

(4) For the given input, AND box provides the Boolean AND output.
True
False

(5) The current in the wire is indicated by 1 and 0 indicates the absence of the current.
True
False

(6) Any language that can not be expressed by a RE is said to be regular language.
True
False

(7) If L1 and L2 are regular languages is/are also regular language(s).

L1 + L2
L1L2
L1
All of above

(8) Let L be a language defined over an alphabet Σ, then the language of strings, defined over Σ, not belonging to L, is called Complement of the language L, denoted by Lc or L.
True False

(9) To describe the complement of a language, it is very important to describe the ----------- of that language over which the language is defined.

Alphabet
Regular Expression
String
Word

(10) For a certain language L, the complement of Lc is the given language L i.e. (Lc)c = Lc
True
False

(11) If L is a regular language then, --------- is also a regular language.
Lm             
Ls               
Lx              
Lc

(12) Converting each of the final states of F to non-final states and old non-final states of F to final states, FA thus obtained will reject every string belonging to L and will accept every string, defined over Σ, not belonging to L. is called

Transition Graph of L
Regular expression of L
Complement of L
Finite Automata of L

(13) If L1 and L2 are two regular languages, then L1 U L2 is not a regular.
True
False


(14) De-Morgan's law for sets is expressed by,








(15) If L1 and L2 are regular languages, then these can be expressed by the corresponding FAs.
True
False

(16) L= language of words containing even number of a’s. Regular Expression is

(a+b)aa(a+b)
(b+aba)
a+bbaaba
(a+b)ab(a+b)

(17) The regular expression defining the language L1 U L2 can be obtained, converting and reducing the previous ------------- into a ------------ as after eliminating states.

GTG, TG
FA, GTG
FA, TG
TG, RE

(18) The language that can be expressed by any regular expression is called a Non regular language.
True
False

(19) The languages -------------- are the examples of non regular languages.

PALINDROME and PRIME
PALINDROME and EVEN-EVEN
EVEN-EVEN and PRIME
FACTORIAL and SQURE

(20) Let L be any infinite regular language, defined over an alphabet Σ then there exist three strings x, y and z belonging to Σsuch that all the strings of the form XY^ n Z for n=1,2,3, … are the words in L. called.

Complement of L
Pumping Lemma
Kleene’s theorem
None in given

(21) Languages are proved to be regular or non regular using pumping lemma.
True
False

(22)    ------------------- is obviously infinite language.
EQUAL-EQUAL
EVEN-EVEN
PALINDROME
FACTORIAL

(23)    If, two strings x and y, defined over Σ, are run over an FA accepting the language L, then x and y are said to belong to the same class if they end in the same state, no matter that state is final or not.
True           
False

Myhill Nerode theorem is consisting of the followings,

L partitions Σinto distinct classes.
If L is regular then, L generates finite number of classes.
If L generates finite number of classes then L is regular.
All of above

The language Q is said to be quotient of two regular languages P and R, denoted by--- if PQ=R.         
R=Q/P       
Q=R/P       
Q=P/R       
P=R/Q



If two languages R and Q are given, then the prefixes of Q in R denoted by Pref(Q in R).
True           
False

(27)    Let Q = {aa, abaaabb, bbaaaaa, bbbbbbbbbb} and R = {b, bbbb, bbbaaa, bbbaaaaa}             
Pref (Q in R) is equal to,

{b,bbba,bbbaaa}
{b,bba,bbaaa}
{ab,bba,bbbaa}
{b,bba,bbba}

If R is regular language and Q is any language (regular/ non regular), then Pref (Q in R) is ---------.

Non-regular
Equal
Regular
Infinite

"CFG" stands for _________

Context Free Graph
Context Free Grammar
Context Finite Graph
Context Finite Grammar

(29)    ___________ states are called the halt states.

ACCEPT and REJECT
ACCEPT and READ
ACCEPT AND START
ACCEPT AND WRITE

(30)    The part of an FA, where the input string is placed before it is run, is called _______

State
Transition
Input Tape
Output Tape

In new format of an FA (discussed in lecture 37), This state is like dead-end non final state

ACCEPT
REJECT
STATR
READ

For language L defined over {a, b}, then L partitions {a, b}into …… classes

Infinite
Finite
Distinct
Non-distinct

The major problem in the earliest computers was

To store the contents in the registers
To display mathematical formulae
To load the contents from the registers
To calculate the mathematical formula

Between the two consecutive joints on a path

One character can be pushed and one character can be popped
Any no. of characters can be pushed and one character can be popped
One character can be pushed and any no. of characters can be popped
Any no. of characters can be pushed and any no. of characters can be popped



(35)    In pumping lemma theorem (x y^n z) the range of n is

n=1, 2, 3, 4……….
n=0, 1, 2, 3, 4……….
n=…….-3,-2,-1, 0, 1, 2, 3, 4……
n=…….-3,-2,-1, 1, 2, 3, 4……

(36)    The PDA is called non-deterministic PDA when there are more than one out going edges from……… state

START or READ
POP or REJECT
READ or POP
PUSH or POP

Identify the TRUE statement:

A PDA is non-deterministic, if there are more than one READ states in PDA
A PDA is never non-deterministic
Like TG, A PDA can also be non-deterministic
A PDA is non-deterministic, if there are more than one REJECT states in PDA

There is a problem in deciding whether a state of FA should be marked or not when the language Q is infinite.

True 
False

If an effectively solvable problem has answered in yes or no, then this solution is called ---------

Decision procedure
Decision method
Decision problem
Decision making

The following problem(s) ------------- is/are called decidable problem(s).

The two regular expressions define the same language
The two FAs are equivalent
Both a and b
None of given

To examine whether a certain FA accepts any words, it is required to seek the paths from ------- state.

Final to initial
Final to final
Initial to final
Initial to initial

The high level language is converted into assembly language codes by a program called compiler.

TRUE
FALSE

Grammatical rules which involve the meaning of words are called ---------------

Semantics
Syntactic
Both a and b
None of given

Grammatical rules which do not involve the meaning of words are called ---------------

Semantics
Syntactic
Both a and b
None of given



The symbols that can’t be replaced by anything are called -----------------
Productions
Terminals
Non-terminals
All of above

The symbols that must be replaced by other things are called __________

Productions
Terminals
Non-terminals
None of given

(47)    The grammatical rules are often called_____________

Productions
Terminals
Non-terminals
None of given

The terminals are designated by ________ letters, while the non-terminals are designated by ________ letters.

Capital, bold
Small, capital
Capital, small
Small, bold

The language generated by __________ is called Context Free Language (CFL).

FA              
TG              
CFG           
TGT

(49)    Σ = {a,b} Productions SXaaX          XaX                   XbX                   X→Λ
This grammar defines the language expressed by___________

(a+b)aa(a+b)
(a+b)a(a+b)a
(a+b)aa(a+b)aa
(a+b)aba+b)

(50)    S aXb|b  XaX aX|bX|Λ The given CFG generates the language in English __________

Beginning and ending in different letters
Beginning and ending in same letter
Having even-even language
None of given

(51)    The CFG is not said to be ambiguous if there exists atleast one word of its language that can be generated by the different production trees,

TRUE                   
FALSE

The language generated by that CFG is regular  if _________

No terminal semi word
No terminal word
Both a and b
None of given

The production of the form no terminal → Λ is said to be null production.

TRUE                   
FALSE

(54)    A production is called null able production if it is of the form N → Λ

TRUE                   
FALSE

(55)    The productions of the form nonterminal one nonterminal, is called _________

Null production
Unit production
Null able production
None of given

(56)    CNF is stands for

Context Normal Form
Complete Normal Form
Chomsky Normal Form
Compared Null Form

Proof(Kleene’s Theorem Part II)
 If a TG has more than one start states, then

Introduce the new start state
Eliminate the old start state
Replace the old start state with final state
Replace the old final state with new start state


Question # 2
While finding RE corresponding to TG, we connect the new start state to the old start state by the transition labeled by
Select correct option:
a
b
null string
None of the given options

Question # 3 of 10 ( Start time: 05:49:03 PM ) Total Marks: 1
Which of the following regular expression represents same language? a. (a+ab)b. (ba+a)c. a(aab)d. (ab)
a+b)a(a+b)b(a+b)+ (a+b)b(a+b)a(a+b).

{ x}, { x}+, {a+b}

Select correct option:
a and b
a and c
c and d

Question # 4 of 10 ( Start time: 05:50:32 PM ) Total Marks: 1
(a+ b)= (a + b)this expression is __________
Select correct option:
True
False

Question # 5 of 10 ( Start time: 05:51:30 PM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must correspond to the initial state of
Select correct option:
FA1 only
FA2 only
FA1 or FA2
FA1 and FA2

Question # 6 of 10 ( Start time: 05:53:01 PM ) Total Marks: 1
Which of the following statement is NOT true about TG?
Select correct option:
There exists exactly one path for certain string
There may exist more than one paths for certain string
There may exist no path for certain string
There may be no final state

Question # 7 of 10 ( Start time: 05:54:06 PM ) Total Marks: 1
Kleene’s theorem states
Select correct option:
All representations of a regular language are equivalent.
All representations of a context free language are equivalent.
All representations of a recursive language are equivalent
Finite Automata are less powerful than Pushdown Automata.


Question # 8 of 10 (Start time: 05:55:36 PM) Total Marks: 1
What do automata mean?
Select correct option:
Something done manually
Something done automatically

Question # 9 of 10 ( Start time: 05:56:51 PM ) Total Marks: 1
A language accepted by an FA is also accepted by
Select correct option:
TG only
GTG only
RE only
All of the given

Question # 10 of 10 ( Start time: 05:58:16 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Select correct option:
(r1)(r2)
(r1 + r2)
(r2)(r1)
(r1)

Question No: 1    ( Marks: 1 )    - Please choose one
 
 If r1 = (aa + bb) and r2 = ( a + b) then the language (aa + bb)(a + b) will be generated by
       ► (r1)(r2)
       ► (r1 + r2)
       ► (r2)(r1)
       ► (r1)
   
Question No: 2    ( Marks: 1 )    - Please choose one
 
 “One language can be expressed by more than one FA”. This statement is ______
       ► True
       ► False
       ► Some times true & sometimes false
       ► None of these
   
Question No: 3    ( Marks: 1 )    - Please choose one
 
 Who did not invent the Turing machine?
       ► Alan Turing
       ► A. M. Turing
       ► Turing
       ► None of these
   
Question No: 4    ( Marks: 1 )- Please choose one
  
Which statement is true?
       ► The tape of turing machine is infinite.
       ► The tape of turing machine is finite.
       ► The tape of turing machine is infinite when the language is regular
       ► The tape of turing machine is finite when the language is nonregular.
   
Question No: 5    ( Marks: 1 )    - Please choose one
  
A regular language:
       ► Must be finite
       ► Must be infinite
       ► Can be finite or infinite
       ► Must be finite and cannot be infinite
   
Question No: 6    ( Marks: 1 )    - Please choose one
  
Every regular expression can be expressed as CFG but every CFG cannot be expressed as a regular expression. This statement is:
       ► Depends on the language
       ► None of the given options
       ► True
       ► False
   
Question No: 7    ( Marks: 1 )    - Please choose one
 
Above given FA corresponds RE r. then FA corresponding to rwill be








This statement is
       True
       False
       Depends on language
       None of these
   
Question No: 8    ( Marks: 1 )    - Please choose one
  
Consider the language L of strings, defined over Σ = {a,b}, ending in a
       There are finite many classes generated by L, so L is regular
       There are infinite many classes generated by L, so L is regular
       There are finite many classes generated by L, so L is non-regular
       There are infinite many classes generated by L, so L is non-regular
   
Question No: 9    ( Marks: 1 )    - Please choose one
 
Above given TG has _____________ RE.
       ► (aa+aa+(ab+ab)(aa+ab)(ab+ba))
       ► (aa+bb+(ab+ba)(aa+bb)(ab+ba))
       ► (aa+bb+(ab+ba)(aa+bb)(ab+ba))
       ► None of these
   
Question No: 10    ( Marks: 1 )    - Please choose one
  
The word ‘formal’ in formal languages means
       ► The symbols used have well defined meaning
       ► They are unnecessary, in reality
       ► Only the form of the string of symbols is significant
       ► None of these
   
Question No: 11    ( Marks: 1 )    - Please choose one
  
Let A = {0, 1}. The number of possible strings of length ‘n’ that can be formed by the elements of the set A is
       ► n!
         n2
       ► nm
       ► 2n
   
Question No: 12    ( Marks: 1 )    - Please choose one
 
 Choose the correct statement.
       ► A Mealy machine generates no language as such
       ► A Moore machine generates no language as such
       ► A Mealy machine has no terminal state
       ► All of these
   
Question No: 13    ( Marks: 1 )    - Please choose one
 
 TM is more powerful than FSM because
       ► The tape movement is confined to one direction
       ► It has no finite state control
       ► It has the capability to remember arbitrary long sequences of input symbols
       ► None of these
   
Question No: 14    ( Marks: 1 )    - Please choose one
 
 If L1 and L2 are expressed by regular expressions r1 and  r2, respectively then the language expressed by  r1 + r2 will be _________
       ► Regular
       ► Ir-regular
       ► Can’t be decided
       ► Another Language which is not listed here
   
Question No: 15    ( Marks: 1 )    - Please choose one
  
Like TG, a PDA can also be non-deterministic
       ► True
       ► False
   
Question No: 16    ( Marks: 1 )    - Please choose one
 

The above machine is a/anTG ___________
       ► Finite Automata
       ► Turing machine
       ► FA
       ► TG
   
Question No: 17    ( Marks: 1 )    - Please choose one
  
The language of all words (made up of a’s and b’s) with at least two a’s can not be described by the regular expression.
       ► a(a+b)a(a+b)(a+b)ab
       ► (a+b)aba(a+b)
       ► baba(a+b)
       ► none of these
   
Question No: 18    ( Marks: 1 )    - Please choose one
  
In FA, if one enters in a specific state but there is no way to leave it, then that specific state is called
                            ► Dead State
       ► Waste Basket
       ► Davey John Locker
       ► All of these
   
Question No: 19    ( Marks: 1 )    - Please choose one
  
If L is a regular language then, Lc is also a _____ language.
       Regular
       ► Non-regular
       ► Regular but finite
       ► None of the given
   
Question No: 20    ( Marks: 1 )    - Please choose one
  
In CFG, the symbols that can’t be replaced by anything are called___
       ► Terminal
       ► Non-Terminal
       ► Production
       ► All of given
   
Question No: 21    ( Marks: 1 )    - Please choose one
  
Which of the following is NOT a regular language?
       ► String of 0’s whose length is a perfect squere
       ► Set of all palindromes made up of 0’s and 1’s
       ► String of 0’s whose length is a prime number
       ► All of the given options
   
Question No: 22    ( Marks: 1 )    - Please choose one
  
Choose the incorrect (FALSE)  statement.
       ► A Mealy machine generates no language as such
       ► A Mealy machine has no terminal state
       ► For a given input string, length of the output string generated by a Moore        machine is not more than the length of the output string generated by that of a Mealy   machine
       ► All of these
   
Question No: 23    ( Marks: 1 )    - Please choose one
 
 Pumping lemma is generally used to prove that:
       ► A given language is infinite
       ► A given language is not regular
       ► Whether two given regular expressions of a regular language are equivalent or not
       ► None of these
   
Question No: 24    ( Marks: 1 )    - Please choose one
  
Which of the following is a regular language?
       ► String of odd number of zeroes
       ► Set of all palindromes made up of 0’s and 1’s
       ► String of 0’s whose length is a prime number
       ► All of these
   
Question No: 25    ( Marks: 1 )    - Please choose one
  
Choose the incorrect statement:
       ► (a+b)aa(a+b)generates Regular language.
       ► A language consisting of all strings over ∑={a,b} having equal number of a’s and b’s  is a regular language
       ► Every language that can be expressed by  FA can also be expressed by RE
       ► None of these
   
Question No: 26    ( Marks: 1 )    - Please choose one
 
 Left hand side of a production in CFG consists of:
       ► One terminal
       ► More than one terminal
       ► One non-terminal
       ► Terminals and non-terminals

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