Technology mapping
Beginner
Choosing real parts from the catalog to build each piece of the simplified circuit.
Novice
Rebuilding the optimized logic out of cells from the target library, keeping the function the same while making the result small, fast or both.
Expert
A covering problem: tile the optimized logic graph (today usually an AIG) with library cells. Modern mappers list the small sub-networks (cuts) ending at each node, look up which cells compute the same function, pick the fastest cover by dynamic programming, then swap in smaller cells away from the critical path.
Explained in Logic synthesis (Design Flow).
See also: And-Inverter Graph (AIG), Liberty (.lib).