During composition we retain intermediate paths like M i 23 utilizing the ability to do lazy composition (Mohri and Pereira, 1998) in order to facilitate beam search through the multi-alignment.
we build our final machine by composing the three sub-machines as, where i = c or i = c + t. This gives us a combined weighted graph by mapping the output symbols of the first medical event sequence to the input symbols of the second medical event sequence.