Take the 2-minute tour ×
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It's 100% free, no registration required.

I received the following assignment:

$\text{EXACT-TRIPLE} = \{ \phi \mid \phi \text{ is a boolean formula that has exactly 3 satisfying assignments} \}$.

I need to decide whether this problem belongs to NP or not. I assume it does not. How do I prove that?

share|improve this question
2  
Are you shure that the assignment doesn't have a third option "Unknown"? :) –  Vor Dec 25 '12 at 18:23

1 Answer 1

The problem is coNP-hard, and so not likely to be in NP. Indeed, given a formula $\phi$, you can construct a formula $\phi'$ such that if $\phi$ has $x$ satisfying assignments then $\phi'$ has $x+3$. This gives a reduction from the coNP-complete problem UN-SAT to EXACT-TRIPLE.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.