On Reversible Transducers

Authors Luc Dartois, Paulin Fournier, Ismaël Jecker, Nathan Lhote

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Luc Dartois
Paulin Fournier
Ismaël Jecker
Nathan Lhote

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Luc Dartois, Paulin Fournier, Ismaël Jecker, and Nathan Lhote. On Reversible Transducers. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 113:1-113:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Deterministic two-way transducers define the robust class of regular functions which is, among other good properties, closed under composition. However, the best known algorithms for composing two-way transducers cause a double exponential blow-up in the size of the inputs. In this paper, we introduce a class of transducers for which the composition has polynomial complexity. It is the class of reversible transducers, for which the computation steps can be reversed deterministically. While in the one-way setting this class is not very expressive, we prove that any two-way transducer can be made reversible through a single exponential blow-up. As a consequence, we prove that the composition of two-way transducers can be done with a single exponential blow-up in the number of states. A uniformization of a relation is a function with the same domain and which is included in the original relation. Our main result actually states that we can uniformize any non-deterministic two-way transducer by a reversible transducer with a single exponential blow-up, improving the known result by de Souza which has a quadruple exponential complexity. As a side result, our construction also gives a quadratic transformation from copyless streaming string transducers to two-way transducers, improving the exponential previous bound.
  • Transducers
  • reversibility
  • two-way
  • uniformization


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