Resynchronizing Classes of Word Relations

Abstract : 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.
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Submitted on : Thursday, April 26, 2018 - 3:38:42 PM
Last modification on : Tuesday, June 12, 2018 - 3:33:07 PM
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María Emilia Descotte, Diego Figueira, Gabriele Puppis. Resynchronizing Classes of Word Relations. International Colloquium on Automata, Languages, and Programming (ICALP), Jul 2018, Prague, Czech Republic. ⟨10.4230/LIPIcs.ICALP.2018.381⟩. ⟨hal-01721046v2⟩

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