On Canonical Models for Rational Functions over Infinite Words

Emmanuel Filiot (1) , Olivier Gauwin (2) , Nathan Lhote (1, 2) , Anca Muscholl (2)

1 ULB - Département d'Informatique [Bruxelles]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

This paper investigates canonical transducers for rational functions over infinite words, i.e., functions of infinite words defined by finite transducers. We first consider sequential functions, defined by finite transducers with a deterministic underlying automaton. We provide a Myhill-Nerode-like characterization, in the vein of Choffrut's result over finite words, from which we derive an algorithm that computes a transducer realizing the function which is minimal and unique (up to the automaton for the domain). The main contribution of the paper is the notion of a canonical transducer for rational functions over infinite words, extending the notion of canonical bimachine due to Reutenauer and Schützenberger from finite to infinite words. As an application, we show that the canonical transducer is aperiodic whenever the function is definable by some aperiodic transducer, or equivalently, by a first-order transduction. This allows to decide whether a rational function of infinite words is first-order definable.

Mots clés: transducers; infinite words; minimization; aperiodicity; first-order logic

Domaines: Théorie et langage formel [cs.FL]; Logique en informatique [cs.LO]

Emmanuel Filiot, Olivier Gauwin, Nathan Lhote, Anca Muscholl. On Canonical Models for Rational Functions over Infinite Words. 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), Dec 2018, Ahmedabad, India. ⟨10.4230/LIPIcs.FSTTCS.2018.30⟩. ⟨hal-01889429⟩