License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.6
URN: urn:nbn:de:0030-drops-95881
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9588/
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Dando, Louis-Marie ; Lombardy, Sylvain

On Hadamard Series and Rotating Q-Automata

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LIPIcs-MFCS-2018-6.pdf (0.5 MB)

Abstract

In this paper, we study rotating Q-automata, which are (memoryless) automata with weights in Q, that can read the input tape from left to right several times. We show that the series realized by valid rotating Q-automata are Q-Hadamard series (which are the closure of Q-rational series by pointwise inverse), and that every Q-Hadamard series can be realized by such an automaton. We prove that, although validity of rotating Q-automata is undecidable, the equivalence problem is decidable on rotating Q-automata. Finally, we prove that every valid two-way Q-automaton admits an equivalent rotating Q-automaton. The conversion, which is effective, implies the decidability of equivalence of two-way Q-automata.

BibTeX - Entry

@InProceedings{dando_et_al:LIPIcs:2018:9588,
  author =	{Louis-Marie Dando and Sylvain Lombardy},
  title =	{{On Hadamard Series and Rotating Q-Automata}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9588},
  URN =		{urn:nbn:de:0030-drops-95881},
  doi =		{10.4230/LIPIcs.MFCS.2018.6},
  annote =	{Keywords: Rational series, Hadamard operations, Rotating automata, Two-way automata}
}

Keywords: Rational series, Hadamard operations, Rotating automata, Two-way automata
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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