  We study randomized and quantum query (a.k.a. decision tree) complexity for
all total Boolean functions, with emphasis to derandomization and
dequantization (removing quantumness from algorithms). Firstly, we show that
$D(f) = O(Q_1(f)^3)$ for any total function $f$, where $D(f)$ is the minimal
number of queries made by a deterministic query algorithm and $Q_1(f)$ is the
number of queries made by any quantum query algorithm (decision tree analog in
quantum case) with one-sided constant error; both algorithms compute function
$f$. Secondly, we show that for all total Boolean functions $f$ holds
$R_0(f)=O(R_2(f)^2 \log N)$, where $R_0(f)$ and $R_2(f)$ are randomized
zero-sided (a.k.a Las Vegas) and two-sided (a.k.a. Monte Carlo) error query
complexities.
