# Serial Composition Of Gotoh Transducers

The composite transducer, $a\stackrel{\Delta T}{\to}b\stackrel{\Delta T}{\to}c$, where $\stackrel{\Delta T}{\to}$ is the Gotoh Transducer. (See Transducer Legend for key.)
We can also consider the jointly normalized HMM that is the composition of the Singlet Transducer with the above composed transducer (c.f. Gotoh Pair HMM). Notationally this is $\epsilon \stackrel{\infty}{\to} a\stackrel{\Delta T}{\to}b\stackrel{\Delta T}{\to}c$, where $\stackrel{\infty}{\to}$ is the Singlet Transducer.