Logics for Word Transductions with Synthesis

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

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.

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