2014/04/25 by Thomas A. Henzinger, Henzinger, Thomas A., Jan Otop +3 · 2 citations
Computer Science · #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #cs.FL
paper · pdf · doi:10.48550/arxiv.1404.6452
In FSTTCS 2014
arxiv created 2014/10/07 · arxiv updated 2014/10/08
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.