Question 1

Recursively enumerable languages are not closed under:

Accepted Answer

A) Union 
B) Intersection 
C) Complementation 
D) Concatenation 
A) Union 
B) Intersection 
C) Complementation 
D) Concatenation C

Question 2

Consider the following statements about the context free grammar G = {S - >SS,S - >ab,S ->ba, S - ?}
I. G is ambiguous
II. G produces all strings with equal number of a's and b's
III. G can be accepted by a deterministic PDA.
Which combination below expresses all the true statements about G?

Accepted Answer

A) 1 only 
B) 1 and 3 
C) 2 and 3 
D) 1,2 and 3 
A) 1 only 
B) 1 and 3 
C) 2 and 3 
D) 1,2 and 3 D

Question 3

Let S be an NP-complete problem, Q and R be two other problems not known to be in NP. Q is polynomial-time reducible to S and S is polynomial-time reducible to R. Which one of the following statements is true?

Accepted Answer

A) R is NP-complete 
B) R is NP-hard 
C) Q is NP-complete 
D) Q is NP-hard 
A) R is NP-complete 
B) R is NP-hard 
C) Q is NP-complete 
D) Q is NP-hard A

Question 4

Give a production grammar for the language L = {x/x ? (a,b)*, the number of a's in x is multiple of 3}.

Accepted Answer

A) {S->bS,S->b,S->aA,S->bA,A->aB,B->bB,B->aS,S->a} 
B) {S->aS,S->bA,A->bB,B->bBa,B->bB} 
C) {S->aaS,S->bbA,A->bB,B->ba} 
D) None of the above 
A) {S->bS,S->b,S->aA,S->bA,A->aB,B->bB,B->aS,S->a} 
B) {S->aS,S->bA,A->bB,B->bBa,B->bB} 
C) {S->aaS,S->bbA,A->bB,B->ba} 
D) None of the above

Question 5

A PC not connected to a network is equivalent to

Accepted Answer

A) A Deterministic Finite-State Automaton, 
B) A Turing Machine, 
C) A Push-Down Automaton, 
D) None of the above. 
A) A Deterministic Finite-State Automaton, 
B) A Turing Machine, 
C) A Push-Down Automaton, 
D) None of the above.

Question 6

A FSM can be considered, having finite tape length without rewinding capability and unidirectional tape movement

Accepted Answer

A) Turing machine 
B) Pushdown automata 
C) Context free languages 
D) Regular languages 
A) Turing machine 
B) Pushdown automata 
C) Context free languages 
D) Regular languages

Question 7

The following CFG is in
S ? Abb
B ? bAA
A ? a
B ? b

Accepted Answer

A) Chomsky normal form but not strong Chomsky normal form 
B) Weak Chomsky normal form but not Chomsky normal form 
C) Strong Chomsky normal form 
D) Greibach normal form 
A) Chomsky normal form but not strong Chomsky normal form 
B) Weak Chomsky normal form but not Chomsky normal form 
C) Strong Chomsky normal form 
D) Greibach normal form

Question 8

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

Accepted Answer

A) State 
B) Transition 
C) Input Tape 
D) Output Tape 
A) State 
B) Transition 
C) Input Tape 
D) Output Tape

Question 9

The production Grammar is {S->aSbb,S->abb} is

Accepted Answer

A) type-3 grammar 
B) type-2 grammar 
C) type-1 grammar 
D) type-0 grammar 
A) type-3 grammar 
B) type-2 grammar 
C) type-1 grammar 
D) type-0 grammar

Question 10

Regular expression (x/y)(x/y) denotes the set

Accepted Answer

A) {xy,xy} 
B) {xx,xy,yx,yy} 
C) {x,y} 
D) {x,y,xy} 
A) {xy,xy} 
B) {xx,xy,yx,yy} 
C) {x,y} 
D) {x,y,xy}

Question 11

Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G =(V,E)with   divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?

Accepted Answer

A) Both DHAM3 and SHAM3 are NP-hard 
B) SHAM3 is NP-hard, but DHAM3 is not 
C) DHAM3 is NP-hard, but SHAM3 is not 
D) Neither DHAM3 nor SHAM3 is NP-hard 
A) Both DHAM3 and SHAM3 are NP-hard 
B) SHAM3 is NP-hard, but DHAM3 is not 
C) DHAM3 is NP-hard, but SHAM3 is not 
D) Neither DHAM3 nor SHAM3 is NP-hard

Question 12

Which of the following statement is true?

Accepted Answer

A) All languages can be generated by CFG 
B) The number of symbols necessary to simulate a Turing Machine(TM) with m symbols and n states is mn. 
C) Any regular languages have an equivalent CFG. 
D) The class of CFG is not closed under union. 
A) All languages can be generated by CFG 
B) The number of symbols necessary to simulate a Turing Machine(TM) with m symbols and n states is mn. 
C) Any regular languages have an equivalent CFG. 
D) The class of CFG is not closed under union.

Question 13

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

Accepted Answer

A) Complement of L 
B) Pumping Lemma 
C) Kleene's theorem 
D) None in given 
A) Complement of L 
B) Pumping Lemma 
C) Kleene's theorem 
D) None in given

Question 14

Recursively enumerable languages are not closed under

Accepted Answer

A) Complementation 
B) Union 
C) Intersection 
D) None of the above 
A) Complementation 
B) Union 
C) Intersection 
D) None of the above

Question 15

Which of the following assertions about Turing Machines is true? Blank symbol(s) may occur in the input. At any stage of a computation, there are only finitely many non-blank Symbols on the tape.

Accepted Answer

A) Assertions (a) and (b) are both true. 
B) Neither (a) nor (b) is true. 
C) Both False 
D) None of above 
A) Assertions (a) and (b) are both true. 
B) Neither (a) nor (b) is true. 
C) Both False 
D) None of above

Question 16

The regular expression have all strings in which any number of 0's is followed by any number of 1's followed by any number of 2's is :

Accepted Answer

A) (0+1+2)* 
B) 0*1*2* 
C) 0* + 1 + 2 
D) (0+1)*2* 
A) (0+1+2)* 
B) 0*1*2* 
C) 0* + 1 + 2 
D) (0+1)*2*

Question 17

For s ? (0+1)* let d(s) denote the decimal value of s(e.g.d(101)) = 5 Let L = {s ? (0+1)* d(s) mod 5=2 and d(s) mod 7 != 4} Which one of the following statements is true?

Accepted Answer

A) L is recursively enumerable, but not recursive 
B) L is recursive, but not context-free 
C) L is context-free, but not regular 
D) L is regular 
A) L is recursively enumerable, but not recursive 
B) L is recursive, but not context-free 
C) L is context-free, but not regular 
D) L is regular

Question 18

Suppose that a problem A is known to have a polynomial-time verification algorithm. Which of the following statements can be deduced.

Accepted Answer

A) A is in NP. 
B) A is in NP but not P 
C) A is in both NP and P. 
D) A is NP-complete. 
A) A is in NP. 
B) A is in NP but not P 
C) A is in both NP and P. 
D) A is NP-complete.

Question 19

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

Accepted Answer

A) Decision procedure 
B) Decision method 
C) Decision problem 
D) Decision making 
A) Decision procedure 
B) Decision method 
C) Decision problem 
D) Decision making

Question 20

Languages are proved to be regular or non regular using pumping lemma.

Accepted Answer

A) True 
B) False 
C) Not always true 
D) can't say anything 
A) True 
B) False 
C) Not always true 
D) can't say anything

Recursively enumerable languages are not closed under:

Consider the following statements about the context free grammar G = {S - >SS,S - >ab,S ->ba, S - ?} I. G is ambiguous II. G produces all strings with equal number of a's and b's III. G can be accepted by a deterministic PDA. Which combination below expresses all the true statements about G?

Let S be an NP-complete problem, Q and R be two other problems not known to be in NP. Q is polynomial-time reducible to S and S is polynomial-time reducible to R. Which one of the following statements is true?

Give a production grammar for the language L = {x/x ? (a,b)*, the number of a's in x is multiple of 3}.

A PC not connected to a network is equivalent to

A FSM can be considered, having finite tape length without rewinding capability and unidirectional tape movement

The following CFG is in S ? Abb B ? bAA A ? a B ? b

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

The production Grammar is {S->aSbb,S->abb} is

Regular expression (x/y)(x/y) denotes the set

Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G =(V,E)with divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?

Which of the following statement is true?

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

Recursively enumerable languages are not closed under

Which of the following assertions about Turing Machines is true? Blank symbol(s) may occur in the input. At any stage of a computation, there are only finitely many non-blank Symbols on the tape.

The regular expression have all strings in which any number of 0's is followed by any number of 1's followed by any number of 2's is :

For s ? (0+1)* let d(s) denote the decimal value of s(e.g.d(101)) = 5 Let L = {s ? (0+1)* d(s) mod 5=2 and d(s) mod 7 != 4} Which one of the following statements is true?

Suppose that a problem A is known to have a polynomial-time verification algorithm. Which of the following statements can be deduced.

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

Languages are proved to be regular or non regular using pumping lemma.

Formal Languages and Automata Theory: Part A

Formal Languages and Automata Theory: Part B

Omputer Science and Theory of Computation

Automata and Turing Machines

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Exam 3: Computational Theory : Grammar, Language, and Complexity

Recursively enumerable languages are not closed under:

Consider the following statements about the context free grammar G = {S - >SS,S - >ab,S ->ba, S - ?} I. G is ambiguous II. G produces all strings with equal number of a's and b's III. G can be accepted by a deterministic PDA. Which combination below expresses all the true statements about G?

Let S be an NP-complete problem, Q and R be two other problems not known to be in NP. Q is polynomial-time reducible to S and S is polynomial-time reducible to R. Which one of the following statements is true?

Give a production grammar for the language L = {x/x ? (a,b)*, the number of a's in x is multiple of 3}.

A PC not connected to a network is equivalent to

A FSM can be considered, having finite tape length without rewinding capability and unidirectional tape movement

The following CFG is in S ? Abb B ? bAA A ? a B ? b

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

The production Grammar is {S->aSbb,S->abb} is

Regular expression (x/y)(x/y) denotes the set

Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G =(V,E)with divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?

Which of the following statement is true?

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

Recursively enumerable languages are not closed under

Which of the following assertions about Turing Machines is true? Blank symbol(s) may occur in the input. At any stage of a computation, there are only finitely many non-blank Symbols on the tape.

The regular expression have all strings in which any number of 0's is followed by any number of 1's followed by any number of 2's is :

For s ? (0+1)* let d(s) denote the decimal value of s(e.g.d(101)) = 5 Let L = {s ? (0+1)* d(s) mod 5=2 and d(s) mod 7 != 4} Which one of the following statements is true?

Suppose that a problem A is known to have a polynomial-time verification algorithm. Which of the following statements can be deduced.

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

Languages are proved to be regular or non regular using pumping lemma.

Formal Languages and Automata Theory: Part A

Formal Languages and Automata Theory: Part B

Omputer Science and Theory of Computation

Automata and Turing Machines

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