  We give a strong direct sum theorem for computing $xor \circ g$.
Specifically, we show that for every function g and every $k\geq 2$, the
randomized query complexity of computing the xor of k instances of g satisfies
$\overline{R}_\eps(xor\circ g) = \Theta(k \overline{R}_{\eps/k}(g))$. This
matches the naive success amplification upper bound and answers a conjecture of
Blais and Brody (CCC19).
  As a consequence of our strong direct sum theorem, we give a total function g
for which $R(xor \circ g) = \Theta(k \log(k)\cdot R(g))$, answering an open
question from Ben-David et al.(arxiv:2006.10957v1).

Computational Complexity