We investigate the problem of checking if a finite-state transducer is robust
to uncertainty in its input. Our notion of robustness is based on the analytic
notion of Lipschitz continuity --- a transducer is K-(Lipschitz) robust if the
perturbation in its output is at most K times the perturbation in its input. We
quantify input and output perturbation using similarity functions. We show that
K-robustness is undecidable even for deterministic transducers. We identify a
class of functional transducers, which admits a polynomial time
automata-theoretic decision procedure for K-robustness. This class includes
Mealy machines and functional letter-to-letter transducers. We also study
K-robustness of nondeterministic transducers. Since a nondeterministic
transducer generates a set of output words for each input word, we quantify
output perturbation using set-similarity functions. We show that K-robustness
of nondeterministic transducers is undecidable, even for letter-to-letter
transducers. We identify a class of set-similarity functions which admit
decidable K-robustness of letter-to-letter transducers.Comment: In FSTTCS 201
