Resynchronizing Classes of Word Relations
Résumé
A natural approach to defining binary word relations over a finite alphabet A is through two-tape finite state automata, which can be seen as regular language L over {1,2}xA, where (i,a) is interpreted as reading letter a from tape i. Thus, a word w of the language L denotes the pair (u_1,u_2) \in A^* \times A^* in which u_i is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of Rational relations (a.k.a. non-deterministic finite state transducers), enforcing restrictions on the reading regime from the tapes, that we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language onto {1,2}. In this way, for each regular language C \subseteq {1,2}^*, one obtains a class Rel(C) of relations, such as the classes of Regular, Recognizable, or length-preserving relations, as well as (infinitely) many other classes.
We study the problem of containment for synchronized classes of relations: given C,D \subseteq {1,2}^*, is Rel(C) \subseteq Rel(D)? We show a characterization in terms of C and D which gives a decidability procedure to test for class inclusion. This also yields a procedure to re-synchronize languages from {1,2}xA preserving the denoted relation whenever the inclusion holds.
Domaines
Théorie et langage formel [cs.FL]
Origine : Fichiers produits par l'(les) auteur(s)
