Talks
Fall 2013 # A Characterization of Strong Approximation Resistance

Monday, Aug. 26, 2013 3:40 pm4:05 pm

For a predicate $f:{-1,1}^k \mapsto {0,1}$ with $\rho(f) = \frac{|f^{-1}(1)|}{2^k}$, we call the predicate strongly approximation resistant if given a near-satisfiable instance of CSP$(f)$, it is computationally hard to find an assignment such that the fraction of constraints satisfied is outside the range $[\rho(f)-\Omega(1), \rho(f)+\Omega(1)]$.
The predicate is called approximation resistant if given a near-satisfiable instance of CSP$(f)$, it is computationally hard to find an assignment such that the fraction of constraints satisfied is at least $\rho(f)+\Omega(1)$. When the predicate is odd, i.e. $f(-z)=1-f(z),\forall z\in {-1,1}^k$, it is easily observed that the notion of approximation resistance coincides with that of strong approximation resistance. Hence for odd predicates, in all the above settings, our characterization of strong approximation resistance is also a characterization of approximation resistance. A Characterization of Strong Approximation Resistance (slides)422.14 KB