## Authors: Luc Dartois, Emmanuel Filiot and Nathan Lhote

## Paper Information

Title: | Logics for Word Transductions with Synthesis |

Authors: | Luc Dartois, Emmanuel Filiot and Nathan Lhote |

Proceedings: | LICS PDF files |

Editors: | Anuj Dawar and Erich GrĂ¤del |

Keywords: | Transduction, Logic, Synthesis, Origin, Data words |

Abstract: | ABSTRACT. We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of the output word, the input position from which it originates. LT is well-suited to express relations (which are not necessarily functional), and can express all regular functional transductions, i.e. transductions definable for instance by deterministic two-way transducers. Despite its high expressive power, LT has decidable satisfiability and equivalence problems, with tight non-elementary and elementary complexities, depending on specific representation of LT-formulas. Our main contribution is a synthesis result: from any transduction R defined in LT, it is possible to synthesise a regular functional transduction f such that for all input words u in the domain of R, f is defined and (u,f(u)) is in R. As a consequence, we obtain that any functional transduction is regular iff it is LT-definable. We also investigate the algorithmic and expressiveness properties of several extensions of LT, and explicit a correspondence between transductions and data words. As a side-result, we obtain a new decidable logic for data words. |

Pages: | 10 |

Talk: | Jul 10 14:40 (Session 55D) |

Paper: |