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Choose the correct statement(s)

A. A problem which is NP-Complete will have the property that it can be solved in polynomial time iff all other NP-complete problems can also be solved in polynomial time.

B. All NP-complete problem are NP-hard problems.

C. If an NP-hard problem can be solved in polynomial time, then all NP-complete problem can be solved in polynomial time

D. All NP-hard-problems are not NP-complete.

Choose the correct answer from the options given below:

  1. A, C only
  2. B, D only
  3. A, B, C only
  4. A, B, C, D

Answer (Detailed Solution Below)

Option 4 : A, B, C, D

Detailed Solution

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More Context Free Languages Questions

Q1.Choose the correct statement(s) A. A problem which is NP-Complete will have the property that it can be solved in polynomial time iff all other NP-complete problems can also be solved in polynomial time. B. All NP-complete problem are NP-hard problems. C. If an NP-hard problem can be solved in polynomial time, then all NP-complete problem can be solved in polynomial time D. All NP-hard-problems are not NP-complete. Choose the correct answer from the options given below:
Q2.What is the safest order while simplifying Context Free Grammar?
Q3.Consider the following statements about Context Free Language (CFL): Statement I: CFL is closed under homomorphism. Statement II: CFL is closed under complement. Which of the following is correct?
Q4.Given below are two statements Statement I : The family of context free languages is closed under homomorphism Statement II : The family of context free languages is closed under reversal In light of the above statements, choose the correct answer from the options given below
Q5.Let L1 = {0n 1n 0m | n >= 1, m >= 1} L2 = {0n 1m 0m | n >= 1, m >= 1} L3 = {0n 1n 0n | n >= 1} Which of the following are correct statements? A. L3 = L1 ∩ L2 B. L1 and L2 are context free languages but L3 is not a context free language C. L1 and L2 are not context free languages but L3 is a context free language D. L1 is a subset of L3 Choose the correct answer from the options given below :
Q6.Consider the following languages: L1 = {ww | w ∈ {a, b}*} L2 = {anbncm | m, n ≥ 0} L3 = {ambncn | m, n ≥ 0} Which of the following statements is/are FALSE?
Q7.Consider the languages L1 = {0i1j | i ≠ j}. L2 = {0i1j | i = j}. L3 = {0i1j | i = 2j + 1}. L4 = {0i1j | i ≠ 2j} Which one of the following statements is true?
Q8.Which of the following statements is true ?
Q9.Consider the following languages : L1 = {am bn | m ≠ n} L2 = {am bn | m = 2n + 1} L3 = {am bn | m ≠ 2n} Which one of the following statement is correct ? 
Q10.Context free grammar is not closed under:

More Context Free Languages and Pushdown Automata Questions

Q1.Let L = L1 ∩ L2 where L1 and L2 are language defined below : L1 = {ambmc an bn m, n ≥ 0} L2 = {aibj ck | i, j, k ≥ 0} Then L is : 
Q2.Consider the grammar with nonterminals N = {S, C, S1} terminals T = {a, b, i, t, e} With S as the start symbol , and the following set of rules : S → i Ct SS1|a S1 → es | ∈ C → b The grammar is not LL(1) because : 
Q3.Which of the following represents the output of the transition function(δ) δ(q0,a) = (q1, x, R) δ(q1,a) = (q1, a, R) δ(q1, y) = (q1, y, R) δ(q1, b) = (q2, y, L) δ(q2, y) = (q2, y, L) δ(q2, a) = (q2, a, L) δ(q2, x) = (q0, x, R) δ(q0, y) = (q3, y, R) δ(q3, y) = (q3, y, R) δ(q3, ◻) = (qf, ◻, R)
Q4.Choose the correct statement(s) A. A problem which is NP-Complete will have the property that it can be solved in polynomial time iff all other NP-complete problems can also be solved in polynomial time. B. All NP-complete problem are NP-hard problems. C. If an NP-hard problem can be solved in polynomial time, then all NP-complete problem can be solved in polynomial time D. All NP-hard-problems are not NP-complete. Choose the correct answer from the options given below:
Q5.Let A= {a, b} and L = A*. Let x = {anbn, n > 0}. The languages L ∪ X and X are respectively :  
Q6.Consider following statements: A. A context free language is generated by LR(o) grammar if and only if it is accepted by a deterministic pushdown automata and has prefix property B. If M1 is the single tape TM simulating multilape TM M, then time taken by M1 to simulate n moves is (n3) C. Push down automata behaves like a Turning machine when it has one auxiliary memory. D. L= {anbncn : n ≥ 1} is not context free but context sensitive. Choose the correct answer from the options given below:
Q7.The maximum yield length of the following CNF CFG is S → AB A → CD B → e C → a D → b
Q8.Which of the following statement is correct? 
Q9.What is the safest order while simplifying Context Free Grammar?
Q10.Match the following based on the language accepted by using brute force method of parsing. LIST - I LIST - II A. S → aSa | aa I. ((2n * 3) - 4) ; n ≥ 1 B. S → aaSaa | aa II. 2n ; n ≥ 1 C. S → aaaSaaa | aa III. ((4 * 2n) - 6) ; n ≥ 1 D. S → aaaaSaaaa | aa IV. 2n - 2 ; n ≥ 2 Choose the correct answer from the options given below: 

More Theory of Computation Questions

Q1.Consider the finite automata given below : The language b accepted by this automata is given by the regular expression :
Q2.Let L = L1 ∩ L2 where L1 and L2 are language defined below : L1 = {ambmc an bn m, n ≥ 0} L2 = {aibj ck | i, j, k ≥ 0} Then L is : 
Q3.If T1 and T2 are two Turing machines. The composite can be represented using the expression :
Q4.__________ is the most general phase structured grammar.
Q5.Consider the grammar with nonterminals N = {S, C, S1} terminals T = {a, b, i, t, e} With S as the start symbol , and the following set of rules : S → i Ct SS1|a S1 → es | ∈ C → b The grammar is not LL(1) because : 
Q6.Which of the following problems is undecidable ? 
Q7.Which of the following represented the minimum state DFA for the above specified passage?
Q8.For the above specified passage, which of the following represent the grammar for the language accepted the machine?
Q9.For the above mentioned passage which of the following is correct?
Q10.For the above specified passage, which of the following represents the regular expression?
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