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?

Related MCQs

• Let L1 be a recursive language. Let L2 and L3 be languages that are recursively enumerable but not recursive. Which of the following statements is not necessarily true?
• For s Є (0+1)* let d(s) denote the decimal value of s(e.g.d(101)) = 5 Let L = {s Є (0+1)* d(s) mod 5=2 and d(s) mod 7 != 4} Which one of the following statements is true?
• Consider the NFA M shown below. Let the language accepted by M be L. Let L1 be the language accepted by the NFA M1, obtained by changing the accepting state of M to a non-accepting state and by changing the non-accepting state of M to accepting states. Which of the following statements is true?
• Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G =(V,E)with V 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?
• 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?
• Let L1 be a recursive language, and let L2 be a recursively enumerable but not a recursive language. Which one of the following is TRUE?
• 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.
• Let P be a regular language and Q be context-free language such that Q ∈ P. (For example, let P be the language represented by the regular expression p*q* and Q be {pnqn n∈ N}). Then which of the following is ALWAYS regular?
• Let w be any string of length n is {0,1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?
• 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.