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In this paper we study the separation between the deterministic (classical)query complexity ($D$) and the exact quantum query complexity ($Q_E$) ofseveral Boolean function classes using the parity decision tree method. Wefirst define the Query Friendly (QF) functions on $n$ variables as the oneswith 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 QFfunctions are non-separable. Then we present QF functions for certain othervalues 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 $\frac{n}{2} \leqQ_E(f) \leq \lceil \frac{3n}{4} \rceil$. Our results highlight how differentclasses of Boolean functions can be analyzed for classical-quantum separationexploiting the parity decision tree method.

Classical-Quantum Separations in Certain Classes of Boolean Functions-- Analysis using the Parity Decision Trees