A Strong XOR Lemma for Randomized Query Complexity.

2020 
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).
    • Correction
    • Source
    • Cite
    • Save
    • Machine Reading By IdeaReader
    0
    References
    0
    Citations
    NaN
    KQI
    []