Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science 2016
DOI: 10.1145/2933575.2934520
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First-order definability of rational transductions

Abstract: The algebraic theory of rational languages has provided powerful decidability results. Among them, one of the most fundamental is the definability of a rational language in the class of aperiodic languages, i.e., languages recognized by finite automata whose transition relation defines an aperiodic congruence. An important corollary of this result is the first-order definability of monadic second-order formulas over finite words. Our goal is to extend these results to rational transductions, i.e. word function… Show more

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Cited by 8 publications
(5 citation statements)
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“…First-order definable transductions were shown to be equivalent to transductions defined by aperiodic streaming transducers [11] and to aperiodic two-way transducers [12]. An effective characterization of aperiodicity for one-way transducers was obtained in [13].…”
Section: Introductionmentioning
confidence: 99%
“…First-order definable transductions were shown to be equivalent to transductions defined by aperiodic streaming transducers [11] and to aperiodic two-way transducers [12]. An effective characterization of aperiodicity for one-way transducers was obtained in [13].…”
Section: Introductionmentioning
confidence: 99%
“…Note that in [FGL16b] we had chosen the term of congruence variety instead of congruence class which was ill-suited, as was kindly pointed out by Jean-Éric Pin, since the term variety stems from an equational theory, which does not exist in a context as general as the one of congruence classes. 1.2.3.…”
Section: Congruence Classesmentioning
confidence: 99%
“…The results of Reutenauer and Schützenberger [20] can indeed be seen as the starting point of two distinct algebraic theories for rational functions; on the one hand the study of continuity, and on the other the study of the transition monoid of the transducer (disregarding the output). This latter avenue was explored by [8]. We show in Section 4.1:…”
Section: Introductionmentioning
confidence: 99%