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Documents authored by Douéneau-Tabot, Gaëtan

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
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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