The two-way quantum/classical finite automaton (2QCFA), defined by Ambainis and Watrous, is a model of quantum computation whose quantum part is extremely limited; however, as they showed, 2QCFA are surprisingly powerful: a 2QCFA, with a single qubit, can recognize, with one-sided bounded-error, the language $L_{eq}=\{a^m b^m |m \in \mathbb{N}\}$ in ... more >>>

Over the last twenty years, an exciting interplay has emerged between proof systems and algorithms. Some natural families of algorithms can be viewed as a generic translation from a proof that a solution exists into an algorithm for finding the solution itself. This connection has perhaps been the most consequential ... more >>>

Given an unpredictable Boolean function $f: \{0, 1\}^n \rightarrow \{0, 1\}$, the standard Yao's XOR lemma is a statement about the unpredictability of computing $\oplus_{i \in [k]}f(x_i)$ given $x_1, ..., x_k \in \{0, 1\}^n$, whereas the Selective XOR lemma is a statement about the unpredictability of computing $\oplus_{i \in S}f(x_i)$ ... more >>>