patternModerate
Is 2-DNF NP-complete?
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Problem
I want to know whether the 2-DNF problem is NP-complete or not? If it is NP-complete, can anyone provide a proof?
Solution
If you are referring to the problem of deciding whether a formula given in 2-DNF form is satisfiable, then it is in $P$, as well as general DNF satisfiability. Indeed, such a formula is satisfiable iff there is a clause that does not contain an inner contradiction. That is, a clause that does not contain both $p$ and $\neg p$ for some atomic proposition $p$. This can be checked in linear time.
Perhaps you are referring to 2-CNF? (Which is also in $P$, but it's less trivial.)
Perhaps you are referring to 2-CNF? (Which is also in $P$, but it's less trivial.)
Context
StackExchange Computer Science Q#9927, answer score: 14
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