Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $ { L }_{ \varepsilon }$ to be the language of all 2CNF formulas $\varphi $, such that at least $(\frac { 1 }{ 2 } + \varepsilon )$ of $\varphi$ 's clauses can be satisfied. Prove that there exists ${ \varepsilon }' > 0$ s.t. ${ L }_{ \varepsilon }$ is NP-hard for any $\varepsilon <\varepsilon '$.

I know that $gap-2SAT\left[ \frac { 3 }{ 4 } ,1 \right]$ is in P thus $\frac { 3 }{ 4 }$ -approximation of max2SAT is in P, so if i chose very small constant $\varepsilon$ such that $\frac { 1 }{ 2 } <\frac { 1 }{ 2 } +\varepsilon <\frac { 3 }{ 4 } $ then the statement above is wrong(there is no such ${ \varepsilon }'$).

Any help would be appreciated.

share|improve this question

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.