par Jecker, Ismaël Robin 
;Filiot, Emmanuel
Référence International journal of foundations of computer science, 29, 2, page (271-296)
Publication Publié, 2018
;Filiot, Emmanuel Référence International journal of foundations of computer science, 29, 2, page (271-296)
Publication Publié, 2018
Article révisé par les pairs
| Résumé : | Rational relations are binary relations of finite words that are realised by non-deterministic finite state transducers (NFT). A multi-sequential relation is a rational relation which is equal to a finite union of (graphs) of partial sequential functions, i.e. functions realised by input-deterministic transducers. The particular case of multi-sequential functions was studied by Choffrut and Schützenberger who proved that given a rational function (as a transducer), it is decidable whether it is multi-sequential. Their procedure is based on an effective characterisation of unambiguous transducers that do not define multi-sequential functions, that we call the fork property. In this paper, we show that the fork property also characterises the class of transducers that do not define multi-sequential relations. Moreover, we prove that the fork property can be decided in PTime. This leads to a PTime procedure which, given a transducer, decides whether it defines a multi-sequential relation. |
