Ramsey Theorem is a cornerstone of combinatorics and logic. In its
simplest formulation it says that there is a function $r$ such that
any simple graph with $r(k,s)$ vertices contains either a clique of
size $k$ or an independent set of size $s$. We study the complexity
of proving upper ... more >>>

We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and read-once CNFs and a hitting set generator for width-3 branching programs, all of which achieve near optimal seed-length even in ... more >>>

We investigate the complexity of the syntactic isomorphism problem of CNF Boolean Formulas (CSFI): given two CNF Boolean formulas $\varphi(a_{1},\ldots,a_{n})$ and $\varphi(b_{1},\ldots,b_{n})$ decide whether there exists a permutation of clauses, a permutation of literals and a bijection between their variables such that $\varphi(a_{1},\ldots,a_{n})$ and $\varphi(b_{1},\ldots,b_{n})$ become syntactically identical. We first ... more >>>