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.2016.65
URN: urn:nbn:de:0030-drops-64771
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6477/
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Löding, Christof ; Winter, Sarah

Uniformization Problems for Tree-Automatic Relations and Top-Down Tree Transducers

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LIPIcs-MFCS-2016-65.pdf (0.5 MB)

Abstract

For a given binary relation of finite trees, we consider the
synthesis problem of deciding whether there is a deterministic
top-down tree transducer that uniformizes the relation, and
constructing such a transducer if it exists. A uniformization of a
relation is a function that is contained in the relation and has the
same domain as the relation. It is known that this problem is
decidable if the relation is a deterministic top-down tree-automatic
relation. We show that it becomes undecidable for general
tree-automatic relations (specified by non-deterministic top-down
tree automata). We also exhibit two cases for which the problem
remains decidable. If we restrict the transducers to be
path-preserving, which is a subclass of linear transducers, then the
synthesis problem is decidable for general tree-automatic
relations. If we consider relations that are finite unions of
deterministic top-down tree-automatic relations, then the problem is
decidable for synchronous transducers, which produce exactly one
output symbol in each step (but can be non-linear).

BibTeX - Entry

@InProceedings{lding_et_al:LIPIcs:2016:6477,
  author =	{Christof L{\"o}ding and Sarah Winter},
  title =	{{Uniformization Problems for Tree-Automatic Relations and Top-Down Tree Transducers}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{65:1--65:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6477},
  URN =		{urn:nbn:de:0030-drops-64771},
  doi =		{10.4230/LIPIcs.MFCS.2016.65},
  annote =	{Keywords: tree transducers, tree automatic relation, uniformization}
}

Keywords: tree transducers, tree automatic relation, uniformization
Collection: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue Date: 2016
Date of publication: 19.08.2016

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