## Marks 1

Consider two decision problems $${Q_1},{Q_2}$$ such that $${Q_1}$$ reduces in polynomial time to $$3$$-$$SAT$$ and $$3$$-$$SAT$$ reduces in polynomial...

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 ...

Let $${\pi _A}$$ be a problem that belongs to the class NP. Then which one of the following is TRUE?

Let S be an NP-complete problem and 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 ...

The problems 3-SAT and 2-SAT are

Ram and Shyam have been asked to show that a certain problem Π is NP-complete. Ram shows a polynomial time reduction from the 3-SAT problem to Π, and ...

## Marks 2

Consider the decision problem 2CNFSAT defined as follows:
{ $$\Phi $$ | $$\Phi $$ is a satisfiable propositional formula in CNF with at most two liter...

Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a
given graph. In this scenario, which one of the foll...

The subset-sum problem is defined as follows:
Given a set S of n positive
integers and a positive integer W, determine whether there is a subset of S...

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 ...

Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable. Which one of the following is TRUE?...

Which of the following problems is not NP-hard?