License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ICALP.2017.115
URN: urn:nbn:de:0030-drops-74583
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Cadilhac, Michaƫl ; Carton, Olivier ; Paperman, Charles

Continuity and Rational Functions

LIPIcs-ICALP-2017-115.pdf (0.5 MB)


A word-to-word function is continuous for a class of languages V if its inverse maps V languages to V. This notion provides a basis for an algebraic study of transducers, and was integral to the characterization of the sequential transducers computable in some circuit complexity classes.

Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages. Previous algebraic studies of transducers have focused on the structure of the underlying input automaton, disregarding the output. We propose a comparison of the two algebraic approaches through two questions: When are the automaton structure and the continuity properties related, and when does continuity propagate to superclasses?

BibTeX - Entry

  author =	{Micha{\"e}l Cadilhac and Olivier Carton and Charles Paperman},
  title =	{{Continuity and Rational Functions}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{115:1--115:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-74583},
  doi =		{10.4230/LIPIcs.ICALP.2017.115},
  annote =	{Keywords: Transducers, rational functions, language varieties, continuity}

Keywords: Transducers, rational functions, language varieties, continuity
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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