# Normal form for deterministic (sub)sequential transducers with letter-by-letter outputs

For a project I'm working on, it would seem useful to have a normal form for deterministic (sub)sequential transducers in which the set of states, $Q$, is partitioned into states, $r \in Q_R$, that read a letter from the input tape (but do not write any output) and states, $w \in Q_W$, that write a letter to the output tape (but do not read any input). The goal is to have (inputs and) outputs occur one letter at a time.

In some proofs that I've seen, a similar kind of normal form is used for deterministic pushdown automata. What I'm looking for is papers that use this kind of normal form in the context of (sub)sequential transducers. Does anyone know of any references?

Specifically, in the normal form that I'm thinking about, there would be two transition functions, one for each part of the partition $Q = Q_R \cup Q_W$: $$\begin{eqnarray} \delta_R &:& Q_R \times \Sigma \to Q \\ \delta_W &:& Q_W \to \Gamma \times Q \\ \end{eqnarray}$$ To enforce finite output, each cycle in the state-transition graph must contain at least one state from $Q_R$. (For subsequential transducers, I think that one needs another class of "terminal write states" that can be entered from a "read state" only when the input has been completely read.)

I'm not sure what your question is. Tell me if I am mistaken. From what I understand: Given a subsequential transducer, you can easily transform it into your canonical form by replacing every transition $(q,a)\to (p,v)$ into a transition reading $a$ and producing nothing followed by a sequence of transitions reading nothing and producing $v$ one letter at a time.
On the other hand, given such a transducer with $\epsilon$ transitions where all loop read some letter, you can compress the finite $\epsilon$-paths to get to a classical sequential transducer.