Consider the decision problem \(2CNFSAT\) defined as follows: \(\left\{ \phi…

GATE · 2014 · CS · Set 3 · Computer Science & IT

Consider the decision problem 2CNFSAT2CNFSAT defined as follows:

{ϕ∣ϕ is a satisfiable propositional formula in CNF with at most two literals per clause}\left\{ \phi \mid \phi \text{ is a satisfiable propositional formula in CNF with at most two literals per clause}\right\}

For example, ϕ=(x1∨x2)∧(x1∨x3ˉ)∧(x2∨x4)\phi = (x1 \vee x2) \wedge (x1 \vee \bar{x3}) \wedge (x2 \vee x4) is a Boolean formula and it is in 2CNFSAT2CNFSAT.

The decision problem 2CNFSAT2CNFSAT is

  1. A.

    NP-Complete.

  2. B.

    solvable in polynomial time by reduction to directed graph reachability.

  3. C.

    solvable in constant time since any input instance is satisfiable.

  4. D.

    NP-hard, but not NP-complete.

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