GATE | GATE-CS-2014-(Set-3) | Question 48

Consider the decision problem 2CNFSAT defined as follows:

GATECS2014Q55

(A) NP-Complete.
(B) solvable in polynomial time by reduction to directed graph reachability.
(C) solvable in constant time since any input instance is satisfiable.
(D) NP-hard, but not NP-complete.


Answer: (B)

Explanation: 2CNF-SAT can be reduced to strongly connected components problem. And strongly connected component has a polynomial time solution. Therefore 2CNF-SAT is polynomial time solvable. See https://en.wikipedia.org/wiki/2-satisfiability#Strongly_connected_components for details.

As a side note, 3CNFSAT is NP Complete problem.

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