CS402- Theory of Automata Solved Final Term Paper 2010

FINALTERM  EXAMINATION

Spring 2010

CS402- Theory of Automata (Session - 1)

Time: 90 min

Marks: 58

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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

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Question No: 4    ( Marks: 1 ) By : Adeel Abbas   - 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

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Question No: 7    ( Marks: 1 )    - Please choose one

Above given FA corresponds RE r. then FA corresponding to r* will be

This statement is

                                   *► True

       ► False

       ► Depends on language

       ► None of these

   

Question No: 8    ( Marks: 1 )    By : Adeel Abbas- 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

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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

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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

       ► n^m

       ► 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

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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

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Question No: 16    ( Marks: 1 )    - Please choose one

The above machine is a/anTG ___________

       ► Finite Automata

                            *► Turing machine

       ► FA

       ► TG

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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)* ab* a(a+b)*

       ► b*ab* a(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, L^c 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

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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

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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

   

Question No: 27    ( Marks: 2 )

 Diffrentiate between Regular and Non regular languages?

Ans:

The main difference between regular and non regular language are as:

1. The regular language is that language which can be expressed by RE is known as regular language whereas any language which can not be expressed by RE is known as non regular language.

   

Question No: 28  ( Marks: 2 )

 What is meant by a "Transition" in FA?

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Question No: 29    ( Marks: 2 )

 What are the halt states of PDAs?

Ans:

There are some halts states in PDA which are as:

1. Accept or reject stat is also halt state.
2. Reject state is like dead non final state.
3. Accept state is like final state.

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Question No: 30    ( Marks: 2 )

 Identify the null productions and nullable productions from the following CFG:

S -> ABAB

A -> a | /\

B-> b | /\

   

Question No: 31    ( Marks: 3 )

 Describe the POP operation and draw symbol for POP state in context of Push down stack.

   

Question No: 32    ( Marks: 3 )

 What does the the following tape of turing machine show?

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Ans:

 Arbitrary Summary Table:

The arbitrary summary table shows the trip from READ9 to READ3 does not pop one

letter form the STACK it adds two letters to the STACK.

Row11 can be concatenated with some other net style sentences e.g. row11 net(READ3, READ7, a)Net(READ7, READ1, b)Net(READ1, READ8, b) it gives the non terminal Net(READ9, READ8, b),

The whole process can be written as:

Net(READ9, READ8, b) ?Row11Net(READ3, READ7,a) Net(READ7, READ1, b)Net(READ1, READ8, b)

This will be a production in the CFG of the corresponding row language.

   

Question No: 33    ( Marks: 3 )

 Find Pref (Q in R) for:

Q = {10, 11, 00, 010}

R = {01001, 10010, 0110, 10101, 01100, 001010}

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Question No: 34    ( Marks: 5 )

 Consider the Context Free Grammar (CFG)

S à 0AS | 0

A à S1A | SS | 1a

Show that the word  0000100 can be generated by this CFG by showing the whole derivation starting from S

   

Question No: 35    ( Marks: 5 )

 Consider the language L which is EVEN-EVEN, defined over  Σ = {a,b}. In how many classes does L may partition Σ*. Explain briefly.

   

Question No: 36    ( Marks: 5 )

 What are the conditions (any five) that must be met to know that PDA is in conversion form?

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Ans:

Conversion form of PDA:

A PDA is in conversion form if it has following conditions:

1. The PDA must begin with the sequence

2. There is only one ACCEPT state.

3. Every edge leading out of any READ or HERE state goes directly into a POP state.

4. There are no REJECT states.

5. All branching, deterministic or nondeterministic occurs at READ or HERE         states.

6. The STACK is never popped beneath this $ symbol.

7. No two POPs exist in a row on the same path without a READ or HERE.

8. Right before entering ACCEPT this symbol is popped out and left.

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By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com