2017/01/13 by Luc Dartois, Dartois, Luc, Emmanuel Filiot +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #DNA and Biological Computing #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO) #Natural Language Processing Techniques #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1701.03670
openalex publication_date 2017/01/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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)) belongs to 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.