Continuity and Rational Functions

@inproceedings{Cadilhac2017ContinuityAR,
  title={Continuity and Rational Functions},
  author={Micha{\"e}l Cadilhac and Olivier Carton and Charles Paperman},
  booktitle={ICALP},
  year={2017}
}
A word-to-word function is continuous for a class of languages $\mathcal{V}$ if its inverse maps $\mathcal{V}$-languages to $\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the characterization of the sequential transducers computable in some circuit complexity classes. Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages. Previous algebraic studies of transducers have… 

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