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2 votes
0 answers
408 views

Is Max-2SAT with exactly 3 occurrences per variable APX-hard?

The Max-2SAT problem asks if at least k clauses of a 2CNF formula can be satisfied. The Max-2SAT(at-most-3) problem is the restriction in which every variable occurs in at most 3 clauses (counting ...
9 votes
2 answers
245 views

Find $\epsilon'$ s.t $L_\epsilon$ is $\mathsf{NP}$-hard for any $\epsilon<\epsilon'$

Let $L_\epsilon$ be the language of all $2$-CNF formulas $\varphi$, such that at least $(\frac{1}{2}+\epsilon)$ of $\varphi$'s clauses can be satisfied. I need to prove that there exists $\epsilon'$ ...