  In this paper we study the separation between the deterministic (classical)
query complexity ($D$) and the exact quantum query complexity ($Q_E$) of
several Boolean function classes using the parity decision tree method. We
first define the Query Friendly (QF) functions on $n$ variables as the ones
with minimum deterministic query complexity $(D(f))$. We observe that for each
$n$, there exists a non-separable class of QF functions such that
$D(f)=Q_E(f)$. Further, we show that for some values of $n$, all the QF
functions are non-separable. Then we present QF functions for certain other
values of $n$ where separation can be demonstrated, in particular,
$Q_E(f)=D(f)-1$. In a related effort, we also study the Maiorana McFarland
(M-M) type Bent functions. We show that while for any M-M Bent function $f$ on
$n$ variables $D(f) = n$, separation can be achieved as $\frac{n}{2} \leq
Q_E(f) \leq \lceil \frac{3n}{4} \rceil$. Our results highlight how different
classes of Boolean functions can be analyzed for classical-quantum separation
exploiting the parity decision tree method.
