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.STACS.2020.32
URN: urn:nbn:de:0030-drops-118933
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11893/
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Colcombet, Thomas ; Lombardy, Sylvain

Unambiguous Separators for Tropical Tree Automata

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LIPIcs-STACS-2020-32.pdf (0.4 MB)

Abstract

In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function f and a min-plus automaton (similar) computing a function g such that f ⩽ g, there exists effectively an unambiguous tropical automaton computing h such that f ⩽ h ⩽ g.
This generalizes a result of Lombardy and Mairesse of 2006 stating that series which are both max-plus and min-plus rational are unambiguous. This generalization goes in two directions: trees are considered instead of words, and separation is established instead of characterization (separation implies characterization). The techniques in the two proofs are very different.

BibTeX - Entry

@InProceedings{colcombet_et_al:LIPIcs:2020:11893,
  author =	{Thomas Colcombet and Sylvain Lombardy},
  title =	{{Unambiguous Separators for Tropical Tree Automata}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{32:1--32:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Christophe Paul and Markus Bl{\"a}ser},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11893},
  URN =		{urn:nbn:de:0030-drops-118933},
  doi =		{10.4230/LIPIcs.STACS.2020.32},
  annote =	{Keywords: Tree automata, Tropical semiring, Separation, Unambiguity}
}

Keywords: Tree automata, Tropical semiring, Separation, Unambiguity
Collection: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Issue Date: 2020
Date of publication: 04.03.2020

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