Title: A Composition Theorem for Randomized Query Complexity,
Abstract: Let the randomized query complexity of a relation for error probability
$\epsilon$ be denoted by $R_\epsilon(\cdot)$. We prove that for any relation $f
\subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m
\rightarrow \{0,1\}$, $R_{1/3}(f\circ g^n) = \Omega(R_{4/9}(f)\cdot
R_{1/2-1/n^4}(g))$, where $f \circ g^n$ is the relation obtained by composing
$f$ and $g$. We also show that $R_{1/3}\left(f \circ \left(g^\oplus_{O(\log
n)}\right)^n\right)=\Omega(\log n \cdot R_{4/9}(f) \cdot R_{1/3}(g))$, where
$g^\oplus_{O(\log n)}$ is the function obtained by composing the xor function
on $O(\log n)$ bits and $g^t$.