Lipschitz Robustness of Finite-state Transducers

Authors Thomas A. Henzinger, Jan Otop, Roopsha Samanta

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Thomas A. Henzinger
Jan Otop
Roopsha Samanta

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Thomas A. Henzinger, Jan Otop, and Roopsha Samanta. Lipschitz Robustness of Finite-state Transducers. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 431-443, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


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.
  • Robustness
  • Transducers
  • Weighted Automata


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