  The synthesis of reversible functions has been an intensively studied
research area in the last decade. Since almost all proposed approaches rely on
representations of exponential size (such as truth tables and permutations),
they cannot be applied efficiently to reversible functions with more than 15
variables.
  In this paper, we propose an ancilla-free synthesis approach based on Young
subgroups using symbolic function representations that can efficiently be
implemented with binary decision diagrams (BDDs). As a result, the algorithm
not only allows to synthesize large reversible functions without adding extra
lines, called ancilla, but also leads to significantly smaller circuits
compared to existing approaches.
