eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-05
30:1
30:17
10.4230/LIPIcs.FSTTCS.2018.30
article
On Canonical Models for Rational Functions over Infinite Words
Filiot, Emmanuel
1
Gauwin, Olivier
2
Lhote, Nathan
3
Muscholl, Anca
2
Université Libre de Bruxelles, Belgium
LaBRI, Université de Bordeaux, France
LaBRI, Université de Bordeaux, France and Université Libre de Bruxelles, Belgium
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol122-fsttcs2018/LIPIcs.FSTTCS.2018.30/LIPIcs.FSTTCS.2018.30.pdf
transducers
infinite words
minimization
aperiodicty
first-order logic