There has been considerable interest lately in the complexity of distributions. Recently, Lovett and Viola (CCC 2011) showed that the statistical distance between a uniform distribution over a good code, and any distribution which can be efficiently sampled by a small bounded-depth AC0 circuit, is inverse-polynomially close to one. That ... more >>>

We consider so-called ``incremental'' dynamic programming (DP) algorithms, and are interested in the number of subproblems produced by them. The standard DP algorithm for the n-dimensional Knapsack problem is incremental, and produces nK subproblems, where K is the capacity of the knapsack. We show that any incremental algorithm for this ... more >>>

In this paper, we study the approximability of Max CSP($P$) where $P$ is a Boolean predicate. We prove that assuming Khot's $d$-to-1 Conjecture, if the set of accepting inputs of $P$ strictly contains all inputs with even (or odd) parity, then it is NP-hard to approximate Max CSP($P$) better than ... more >>>