  Reversible computation is gaining increasing relevance in the context of
several post-CMOS technologies, the most prominent of those being Quantum
computing. One of the key theoretical problem pertaining to reversible logic
synthesis is the upper bound of the gate count. Compared to the known bounds,
the results obtained by optimal synthesis methods are significantly less. In
this paper, we connect this problem with the multiplicative complexity analysis
of classical Boolean functions. We explore the possibility of relaxing the
ancilla and if that approach makes the upper bound tighter. Our results are
negative. The ancilla-free synthesis methods by using transformations and by
starting from an Exclusive Sum-of-Product (ESOP) formulation remain,
theoretically, the synthesis methods for achieving least gate count for the
cases where the number of variables $n$ is $< 8$ and otherwise, respectively.
