For a complexity class $C$ and language $L$, a constructive separation of $L \notin C$ gives an efficient algorithm (also called a refuter) to find counterexamples (bad inputs) for every $C$-algorithm attempting to decide $L$. We study the questions: Which lower bounds can be made constructive? What are the consequences ... more >>>

We further the study of supercritical tradeoffs in proof and circuit complexity, which is a type of tradeoff between complexity parameters where restricting one complexity parameter forces another to exceed its worst-case upper bound. In particular, we prove a new family of supercritical tradeoffs between depth and size for Resolution, ... more >>>

Statistics of small subgraph counts such as triangles, four-cycles, and $s$-$t$ paths of short lengths reveal important structural properties of the underlying graph. These problems have been widely studied in social network analysis. In most relevant applications, the graphs are not only massive but also change dynamically over time. Most ... more >>>