πŸ“Š Theory of Computation
Q. Context free grammar is used for-
  • (A) Lexical analyzer
  • (B) Document type definition (DTD)
  • (C) Text pattern searching
  • (D) Both a & c
πŸ’¬ Discuss
βœ… Correct Answer: (B) Document type definition (DTD)
πŸ“Š Theory of Computation
Q. The set strings of 0's and 1's with atmost one pair consecutive one's-
  • (A) (0+1)*(01)(10)(0+1)*
  • (B) (0+1)*(01)*(10)(0+1)*
  • (C) (0+1)*(01)(10)*(0+1)*
  • (D) (0+!)(01)*(10)*(0+1)
πŸ’¬ Discuss
βœ… Correct Answer: (D) (0+!)(01)*(10)*(0+1)
πŸ“Š Theory of Computation
Q. The problem 3-SAT and 2-SAT are
  • (A) Both in P
  • (B) Both NP complete
  • (C) NP-complete and in P respectively
  • (D) Undecidable and NP-complete respectively
πŸ’¬ Discuss
βœ… Correct Answer: (C) NP-complete and in P respectively
πŸ“Š Theory of Computation
Q. Which of the following instances of the post correspondence problem has a viable sequence (a solution)?
  • (A) {(b, bb), (bb, bab), (bab, abb), (abb, babb)}
  • (B) {(ab, aba), (baa, aa), (aba, baa)}
  • (C) {(ab, abb), (ba, aaa), (aa, a)}
  • (D) none of the above
πŸ’¬ Discuss
βœ… Correct Answer: (C) {(ab, abb), (ba, aaa), (aa, a)}
πŸ“Š Theory of Computation
Q. Let FHAM be the problem of finding a Hamiltonian cycle in a graph G and DHAM be the problem of determining if a Hamiltonial cycle exists in a graph. Which one of the following is TRUE?
  • (A) Both FHAM and DHAM are NP-hard
  • (B) FHAM is NP hard, but DHAM is not
  • (C) DHAM is NP hard, but FHAM is not
  • (D) Neither FHAM nor DHAM is NP hard
πŸ’¬ Discuss
βœ… Correct Answer: (A) Both FHAM and DHAM are NP-hard
πŸ“Š Theory of Computation
Q. Consider three problems P1, P2 and P3. It is known that P1 has polynomial time solution and P2 is NP-complete and P3 is in NP. Which one of the following is true.
  • (A) P3 has polynomial time solution if P1 is polynomial time reducible to P3
  • (B) P3 is NP complete if P3 is polynomial time reducible to P2
  • (C) P3 is NP complete if P2 is reducible to P3
  • (D) P3 has polynomial time complexity and P3 is reducible to P2
πŸ’¬ Discuss
βœ… Correct Answer: (C) P3 is NP complete if P2 is reducible to P3
πŸ“Š Theory of Computation
Q. Which one of the following is the strongest correct statement about a finite language Lover a finite alphabet Σ?
  • (A) L is undecidable
  • (B) L is recursive
  • (C) L is a CSL
  • (D) L is a regular set
πŸ’¬ Discuss
βœ… Correct Answer: (D) L is a regular set
πŸ“Š Theory of Computation
Q. Which one of the following is not decidable?
  • (A) given a Turing machine M, a string s, and an integer k, M accepts s with k steps
  • (B) equivalence of two given Turing machines
  • (C) language accepted by a given DFSA is nonempty
  • (D) language generated by a CFG is nonempty
πŸ’¬ Discuss
βœ… Correct Answer: (B) equivalence of two given Turing machines
πŸ“Š Theory of Computation
Q. Which of the following statements are TRUE?
(1) The problem of determining whether there exists a cycle in an undirected graph is in P.
(2) The problem of determining whether there exists a cycle in an undirected graph is in NP.
(3) If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.
  • (A) 1, 2 and 3
  • (B) 1 and 2 only
  • (C) 2 and 3 only
  • (D) 1 and 3 only
πŸ’¬ Discuss
βœ… Correct Answer: (A) 1, 2 and 3
πŸ“Š Theory of Computation
Q. Consider a graph G = (V, E) where I V I is divisible by 3. The problem of finding a Hamiltonian cycle in a graph is denoted by SHAM3 and the problem of determining if a Hamiltonian cycle exits in such graph is denoted by DHAM3. The option, which holds true, is
  • (A) Only DHAM3 is NP-hard
  • (B) Only SHAM3 is NP-hard
  • (C) Both SHAM3 and DHAM3 are NP-hard
  • (D) Neither SHAM3 nor DHAM3 is NP-hard
πŸ’¬ Discuss
βœ… Correct Answer: (C) Both SHAM3 and DHAM3 are NP-hard

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