Two persons X and Y have been asked to show that a certain problem p is NP-complete. X shows a polynomial time reduction from the 3-SAT problem to p and Y shows a polynomial time reduction from p to 3-SAT. From these reduction it can be inferred that

Related MCQs

• 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?
• 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.
• Suppose that a problem A is known to have a polynomial-time verification algorithm. Which of the following statements can be deduced.
• 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.
• Following syntax-directed translation scheme is used with a shift reduction (bottom up) parser that perform the action in braces immediately after a reduction by the corresponding production A —>aB {print “(1)” A —> c {print “1”), B —>Ab {print *2”}. When parser is aaacbbb, then string printed
• 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?
• 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
• Fred created a new automaton model which is a push down automaton but with two stacks and the added ability of having commands which do not read input tape but which can pop from one stack and push into the other.This new automaton can recognize (choose strongest result)
• Which of the following are decidable? 1) Whether the intersection of two regular language is infinite. 2) Whether a given context free language is regular. 3) Whether two push down automata accept the same language. 4) Whether a given grammar is context free.