Question 1 |
The problem 3-SAT and 2-SAT are
both in P | |
both NP complete | |
NP -complete and in P respectively | |
undecidable and NP complete respectively |
Question 1 Explanation:
Question 2 |
Language L_{1} is polynomial time reducible to language L_{2}. Language L_{3} is polynomial time reducible to L_{2}, which in turn is polynomial time reducible to language L_{4}. Which of the following is/are true?
I. if L_{4} \in P, then L_{2} \in P
II. if L_{1} \in P or L_{3} \in P, then L_{2} \in P
III. L_{1} \in P, if and only if L_{3} \in P
IV. if L_{4} \in P, then L_{1} \in P and L_{3} \in P
I. if L_{4} \in P, then L_{2} \in P
II. if L_{1} \in P or L_{3} \in P, then L_{2} \in P
III. L_{1} \in P, if and only if L_{3} \in P
IV. if L_{4} \in P, then L_{1} \in P and L_{3} \in P
II only | |
III only | |
I and IV only | |
I only |
Question 2 Explanation:
Question 3 |
Consider two decision problems Q1,Q2 such that Q1 reduces in polynomial time to 3-SAT and 3-SAT reduces in polynomial time to Q2. Then which one of the following is consistent with the above statement?
Q1 is in NP, Q2 is NP hard. | |
Q2 is in NP, Q1 is NP hard | |
Both Q1 and Q2 are in NP . | |
Both Q1 and Q2 are NP hard |
Question 3 Explanation:
Question 4 |
Consider the decision problem 2CNFSAT defined as follows:
{ \phi | \phi is a satisfiable propositional formula in CNF with at most two literal per clause}
For example, \phi =(x_{1} \vee x_{2}) \wedge (x_{1} \vee \bar{x_{3}}) \wedge (x_{2} \vee x_{4}) is a Boolean formula and it is in 2CNFSAT.
The decision problem 2CNFSAT is
{ \phi | \phi is a satisfiable propositional formula in CNF with at most two literal per clause}
For example, \phi =(x_{1} \vee x_{2}) \wedge (x_{1} \vee \bar{x_{3}}) \wedge (x_{2} \vee x_{4}) is a Boolean formula and it is in 2CNFSAT.
The decision problem 2CNFSAT is
NP-Complete | |
solvable in polynomial time by reduction to directed graph reachability. | |
solvable in constant time since any input instance is satisfiable | |
NP-hard, but not NP-complete |
Question 4 Explanation:
Question 5 |
Suppose a polynomial time algorithm is discovered that correctly computes the largest clique
in a given graph. In this scenario, which one of the following represents the correct Venn
diagram of the complexity classes P, NP and NP Complete (NPC)?


A | |
B | |
C | |
D |
Question 5 Explanation:
There are 5 questions to complete.