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1
One-way definability of two-way word transducers
In: EISSN: 1860-5974 ; Logical Methods in Computer Science ; https://hal.archives-ouvertes.fr/hal-02121085 ; Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2018, 14 (4), ⟨10.23638/LMCS-14(4:22)2018⟩ ; https://lmcs.episciences.org/5021 (2018)
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2
First-order definability of rational transductions: An algebraic approach
In: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS'16) ; 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS'16) ; https://hal.archives-ouvertes.fr/hal-01308509 ; 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS'16), Jul 2016, New York, United States. pp.387--396, ⟨10.1145/2933575.2934520⟩ ; http://lics.rwth-aachen.de/lics16/ (2016)
Abstract: International audience ; 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 functions realized by finite transducers. We take an algebraic approach and consider definability problems of rational transductions in a given variety of congruences (or monoids). The strength of the algebraic theory of rational languages relies on the existence of a congruence canonically attached to every language, the syntactic congruence. In a similar spirit, Reutenauer and Schützenberger have defined a canonical device for rational transductions, that we extend to establish our main contribution: an effective characterization of V-transductions, i.e. rational transductions realizable by transducers whose transition relation defines a congruence in a (decidable) variety V. In particular, it provides an algorithm to decide the definability of a rational transduction by an aperiodic finite transducer. Using those results, we show that the FO-definability of a rational transduction is decidable, where FO-definable means definable in a first-order restriction of logical transducers a la Courcelle.
Keyword: [INFO.INFO-FL]Computer Science [cs]/Formal Languages and Automata Theory [cs.FL]; [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]; ACM: F.: Theory of Computation/F.4: MATHEMATICAL LOGIC AND FORMAL LANGUAGES/F.4.3: Formal Languages; ACM: F.: Theory of Computation/F.4: MATHEMATICAL LOGIC AND FORMAL LANGUAGES/F.4.3: Formal Languages/F.4.3.3: Decision problems; algebraic characterizations; definability problems; first-order logic; rational word transductions
URL: https://hal.archives-ouvertes.fr/hal-01308509/file/main_lics.pdf
https://doi.org/10.1145/2933575.2934520
https://hal.archives-ouvertes.fr/hal-01308509/document
https://hal.archives-ouvertes.fr/hal-01308509
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3
Streaming Tree Automata and XPath ; Flux XML, Requêtes XPath et Automates
Gauwin, Olivier. - : HAL CCSD, 2009
In: https://tel.archives-ouvertes.fr/tel-00421911 ; Software Engineering [cs.SE]. Université des Sciences et Technologie de Lille - Lille I, 2009. English (2009)
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