We characterize the set of properties of Boolean-valued functions on a finite domain $\mathcal{X}$ that are testable with a constant number of samples.
Specifically, we show that a property $\mathcal{P}$ is testable with a constant number of samples if and only if it is (essentially) a $k$-part symmetric property ... more >>>

In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear quantum speedup for some task, motivated by the goal of overturning the Extended Church-Turing Thesis ... more >>>

The class TFNP is the search analog of NP with the additional guarantee that any instance has a solution. TFNP has attracted extensive attention due to its natural syntactic subclasses that capture the computational complexity of important search problems from algorithmic game theory, combinatorial optimization and computational topology. Thus, one ... more >>>