Let $f:\{0,1\}^n \rightarrow \{0,1\}$ be a Boolean function. The certificate complexity $C(f)$ is a complexity measure that is quadratically tight for the zero-error randomized query complexity $R_0(f)$: $C(f) \leq R_0(f) \leq C(f)^2$. In this paper we study a new complexity measure that we call expectational certificate complexity $EC(f)$, which is ... more >>>

A basic question in complexity theory is whether the computational
resources required for solving k independent instances of the same
problem scale as k times the resources required for one instance.
We investigate this question in various models of classical
communication complexity.

We define a new measure, the subdistribution bound, ... more >>>

A strong direct product theorem says that if we want to compute
k independent instances of a function, using less than k times
the resources needed for one instance, then our overall success
probability will be exponentially small in k.
We establish such theorems for the classical as well as ... more >>>

While deterministic finite automata seem to be well understood, surprisingly
many important problems
concerning nondeterministic finite automata (nfa's) remain open.

One such problem area is the study of different measures of nondeterminism in
finite automata and the
estimation of the sizes of minimal nondeterministic finite automata. In this
paper the ... more >>>