9 Search Results for "Douéneau-Tabot, Gaëtan"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.50
Lexicographic Transductions of Finite Words

Authors: Emmanuel Filiot, Nathan Lhote, and Pierre-Alain Reynier

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Regular transductions over finite words have linear input-to-output growth. This class of transductions enjoys many characterizations, such as transductions computable by two-way transducers as well as transductions definable in MSO (in the sense of Courcelle). Recently, regular transductions have been extended by Bojańczyk to polyregular transductions, which have polynomial growth, and are characterized by pebble transducers and MSO interpretations. Another class of interest is that of transductions defined by streaming string transducers or marble transducers, which have exponential growth and are incomparable with polyregular transductions. In this paper, we consider MSO set interpretations (MSOSI) over finite words, that were introduced by Colcombet and Loeding. MSOSI are a natural candidate for the class of "regular transductions with exponential growth", and are rather well behaved. However, MSOSI for now lacks two desirable properties that regular and polyregular transductions have. The first property is to have an automata description. This property is closely related to a second property, that of being regularity preserving, meaning preserving regular languages under inverse image. We first show that if MSOSI are (effectively) regularity preserving then any automatic ω-word has a decidable MSO theory, an almost 20 years old conjecture of Bárány. Our main contribution is the introduction of a class of transductions of exponential growth, which we call lexicographic transductions. We provide three different presentations for this class: first, as the closure of simple transductions (recognizable transductions) under a single operator called maplex; second, as a syntactic fragment of MSOSI (but the regular languages are given by automata instead of formulas); and third, we give an automaton based model called nested marble transducers, which generalize both marble transducers and pebble transducers. We show that this class enjoys many nice properties including being regularity preserving.
Cite as

Emmanuel Filiot, Nathan Lhote, and Pierre-Alain Reynier. Lexicographic Transductions of Finite Words. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{filiot_et_al:LIPIcs.MFCS.2025.50,
  author =	{Filiot, Emmanuel and Lhote, Nathan and Reynier, Pierre-Alain},
  title =	{{Lexicographic Transductions of Finite Words}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{50:1--50:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.50},
  URN =		{urn:nbn:de:0030-drops-241572},
  doi =		{10.4230/LIPIcs.MFCS.2025.50},
  annote =	{Keywords: Transducers, Automata, MSO, Logical interpretations, Automatic structures}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.67
Commutative ℕ-Rational Series of Polynomial Growth

Authors: Aliaume Lopez

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
This paper studies which functions computed by ℤ-weighted automata can be realised by ℕ-weighted automata, under two extra assumptions: commutativity (the order of letters in the input does not matter) and polynomial growth (the output of the function is bounded by a polynomial in the size of the input). We leverage this effective characterization to decide whether a function computed by a commutative ℕ-weighted automaton of polynomial growth is star-free, a notion borrowed from the theory of regular languages that has been the subject of many investigations in the context of string-to-string functions during the last decade.
Cite as

Aliaume Lopez. Commutative ℕ-Rational Series of Polynomial Growth. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 67:1-67:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lopez:LIPIcs.STACS.2025.67,
  author =	{Lopez, Aliaume},
  title =	{{Commutative \mathbb{N}-Rational Series of Polynomial Growth}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{67:1--67:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.67},
  URN =		{urn:nbn:de:0030-drops-228924},
  doi =		{10.4230/LIPIcs.STACS.2025.67},
  annote =	{Keywords: Rational series, weighted automata, polyregular function, commutative}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.121
Deterministic Regular Functions of Infinite Words

Authors: Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller streaming string transducers, and to functions defined by MSO-transductions. Regular functions are however not computable in general (for a classical extension of Turing computability to infinite inputs), and we consider in this paper the class of deterministic regular functions of infinite words, realized by deterministic two-way transducers without look-ahead. We prove that it is a well-behaved class of functions: they are computable, closed under composition, characterized by the guarded fragment of MSO-transductions, by deterministic Büchi streaming string transducers, by deterministic two-way transducers with finite look-ahead, and by finite compositions of sequential functions and one fixed basic function called map-copy-reverse.
Cite as

Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter. Deterministic Regular Functions of Infinite Words. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 121:1-121:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{carton_et_al:LIPIcs.ICALP.2023.121,
  author =	{Carton, Olivier and Dou\'{e}neau-Tabot, Ga\"{e}tan and Filiot, Emmanuel and Winter, Sarah},
  title =	{{Deterministic Regular Functions of Infinite Words}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{121:1--121:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.121},
  URN =		{urn:nbn:de:0030-drops-181733},
  doi =		{10.4230/LIPIcs.ICALP.2023.121},
  annote =	{Keywords: infinite words, streaming string transducers, two-way transducers, monadic second-order logic, look-aheads, factorization forests}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.28
Continuous Rational Functions Are Deterministic Regular

Authors: Olivier Carton and Gaëtan Douéneau-Tabot

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
A word-to-word function is rational if it can be realized by a non-deterministic one-way transducer. Over finite words, it is a classical result that any rational function is regular, i.e. it can be computed by a deterministic two-way transducer, or equivalently, by a deterministic streaming string transducer (a one-way automaton which manipulates string registers). This result no longer holds for infinite words, since a non-deterministic one-way transducer can guess, and check along its run, properties such as infinitely many occurrences of some pattern, which is impossible for a deterministic machine. In this paper, we identify the class of rational functions over infinite words which are also computable by a deterministic two-way transducer. It coincides with the class of rational functions which are continuous, and this property can thus be decided. This solves an open question raised in a previous paper of Dave et al.
Cite as

Olivier Carton and Gaëtan Douéneau-Tabot. Continuous Rational Functions Are Deterministic Regular. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{carton_et_al:LIPIcs.MFCS.2022.28,
  author =	{Carton, Olivier and Dou\'{e}neau-Tabot, Ga\"{e}tan},
  title =	{{Continuous Rational Functions Are Deterministic Regular}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.28},
  URN =		{urn:nbn:de:0030-drops-168268},
  doi =		{10.4230/LIPIcs.MFCS.2022.28},
  annote =	{Keywords: infinite words, rational functions, determinization, continuity, streaming string transducers, two-way transducers}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.120
Hiding Pebbles When the Output Alphabet Is Unary

Authors: Gaëtan Douéneau-Tabot

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Pebble transducers are nested two-way transducers which can drop marks (named "pebbles") on their input word. Blind transducers have been introduced by Nguyên et al. as a subclass of pebble transducers, which can nest two-way transducers but cannot drop pebbles on their input. In this paper, we study the classes of functions computed by pebble and blind transducers, when the output alphabet is unary. Our main result shows how to decide if a function computed by a pebble transducer can be computed by a blind transducer. We also provide characterizations of these classes in terms of Cauchy and Hadamard products, in the spirit of rational series. Furthermore, pumping-like characterizations of the functions computed by blind transducers are given.
Cite as

Gaëtan Douéneau-Tabot. Hiding Pebbles When the Output Alphabet Is Unary. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 120:1-120:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{doueneautabot:LIPIcs.ICALP.2022.120,
  author =	{Dou\'{e}neau-Tabot, Ga\"{e}tan},
  title =	{{Hiding Pebbles When the Output Alphabet Is Unary}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{120:1--120:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.120},
  URN =		{urn:nbn:de:0030-drops-164613},
  doi =		{10.4230/LIPIcs.ICALP.2022.120},
  annote =	{Keywords: polyregular functions, pebble transducers, rational series, factorization forests, Cauchy product, Hadamard product}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.40
Pebble Transducers with Unary Output

Authors: Gaëtan Douéneau-Tabot

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Bojańczyk recently initiated an intensive study of deterministic pebble transducers, which are two-way automata that can drop marks (named "pebbles") on their input word, and produce an output word. They describe functions from words to words. Two natural restrictions of this definition have been investigated: marble transducers by Douéneau-Tabot et al., and comparison-free pebble transducers (that we rename here "blind transducers") by Nguyên et al. Here, we study the decidability of membership problems between the classes of functions computed by pebble, marble and blind transducers that produce a unary output. First, we show that pebble and marble transducers have the same expressive power when the outputs are unary (which is false over non-unary outputs). Then, we characterize 1-pebble transducers with unary output that describe a function computable by a blind transducer, and show that the membership problem is decidable. These results can be interpreted in terms of automated simplification of programs.
Cite as

Gaëtan Douéneau-Tabot. Pebble Transducers with Unary Output. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{doueneautabot:LIPIcs.MFCS.2021.40,
  author =	{Dou\'{e}neau-Tabot, Ga\"{e}tan},
  title =	{{Pebble Transducers with Unary Output}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.40},
  URN =		{urn:nbn:de:0030-drops-144805},
  doi =		{10.4230/LIPIcs.MFCS.2021.40},
  annote =	{Keywords: polyregular functions, pebble transducers, marble transducers, streaming string transducers, factorization forests}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.139
Comparison-Free Polyregular Functions

Authors: Lê Thành Dũng (Tito) Nguyễn, Camille Noûs, and Cécilia Pradic

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
This paper introduces a new automata-theoretic class of string-to-string functions with polynomial growth. Several equivalent definitions are provided: a machine model which is a restricted variant of pebble transducers, and a few inductive definitions that close the class of regular functions under certain operations. Our motivation for studying this class comes from another characterization, which we merely mention here but prove elsewhere, based on a λ-calculus with a linear type system. As their name suggests, these comparison-free polyregular functions form a subclass of polyregular functions; we prove that the inclusion is strict. We also show that they are incomparable with HDT0L transductions, closed under usual function composition - but not under a certain "map" combinator - and satisfy a comparison-free version of the pebble minimization theorem. On the broader topic of polynomial growth transductions, we also consider the recently introduced layered streaming string transducers (SSTs), or equivalently k-marble transducers. We prove that a function can be obtained by composing such transducers together if and only if it is polyregular, and that k-layered SSTs (or k-marble transducers) are closed under "map" and equivalent to a corresponding notion of (k+1)-layered HDT0L systems.
Cite as

Lê Thành Dũng (Tito) Nguyễn, Camille Noûs, and Cécilia Pradic. Comparison-Free Polyregular Functions. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 139:1-139:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{nguyen_et_al:LIPIcs.ICALP.2021.139,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito) and No\^{u}s, Camille and Pradic, C\'{e}cilia},
  title =	{{Comparison-Free Polyregular Functions}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{139:1--139:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.139},
  URN =		{urn:nbn:de:0030-drops-142087},
  doi =		{10.4230/LIPIcs.ICALP.2021.139},
  annote =	{Keywords: pebble transducers, HDT0L systems, polyregular functions}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.29
Register Transducers Are Marble Transducers

Authors: Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Paul Gastin

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
Deterministic two-way transducers define the class of regular functions from words to words. Alur and Cerný introduced an equivalent model of transducers with registers called copyless streaming string transducers. In this paper, we drop the "copyless" restriction on these machines and show that they are equivalent to two-way transducers enhanced with the ability to drop marks, named "marbles", on the input. We relate the maximal number of marbles used with the amount of register copies performed by the streaming string transducer. Finally, we show that the class membership problems associated with these models are decidable. Our results can be interpreted in terms of program optimization for simple recursive and iterative programs.
Cite as

Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Paul Gastin. Register Transducers Are Marble Transducers. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{doueneautabot_et_al:LIPIcs.MFCS.2020.29,
  author =	{Dou\'{e}neau-Tabot, Ga\"{e}tan and Filiot, Emmanuel and Gastin, Paul},
  title =	{{Register Transducers Are Marble Transducers}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{29:1--29:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.29},
  URN =		{urn:nbn:de:0030-drops-126979},
  doi =		{10.4230/LIPIcs.MFCS.2020.29},
  annote =	{Keywords: streaming string transducer, two-way transducer, marbles, pebbles}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.122
On the Complexity of Infinite Advice Strings

Authors: Gaëtan Douéneau-Tabot

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We investigate in this paper a notion of comparison between infinite strings. In a general way, if M is a computation model (e.g. Turing machines) and C a class of objects (e.g. languages), the complexity of an infinite word alpha can be measured with respect to the amount of objects from C that are presentable with machines from M using alpha as an oracle. In our case, the model M is finite automata and the objects C are either recognized languages or presentable structures, known respectively as advice regular languages and advice automatic structures. This leads to several different classifications of infinite words that are studied in detail; we also derive logical and computational equivalent measures. Our main results explore the connections between classes of advice automatic structures, MSO-transductions and two-way transducers. They suggest a closer study of the resulting hierarchy over infinite words.
Cite as

Gaëtan Douéneau-Tabot. On the Complexity of Infinite Advice Strings. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 122:1-122:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{doueneautabot:LIPIcs.ICALP.2018.122,
  author =	{Dou\'{e}neau-Tabot, Ga\"{e}tan},
  title =	{{On the Complexity of Infinite Advice Strings}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{122:1--122:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.122},
  URN =		{urn:nbn:de:0030-drops-91260},
  doi =		{10.4230/LIPIcs.ICALP.2018.122},
  annote =	{Keywords: infinite words, advice automata, automatic structures, transducers}
}
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