  We present new algorithms to synthesize exact universal reversible gate
library for various types of gates and costs. We use the powerful algebraic
software GAP for implementation and examination of our algorithms and the
reversible logic synthesis problems have been reduced to group theory problems.
It is shown that minimization of arbitrary cost functions of gates and orders
of magnitude are faster than its previously counterparts for reversible logic
synthesis. Experimental results show that a significant improvement over the
previously proposed synthesis algorithm is obtained compared with the existing
approaches to reversible logic synthesis.
