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

Authors Christof Löding, Sarah Winter

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Keywords
  • tree transducers
  • tree automatic relation
  • uniformization

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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).

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Christof Löding and Sarah Winter. Uniformization Problems for Tree-Automatic Relations and Top-Down Tree Transducers. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 65:1-65:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.MFCS.2016.65

Author Details

Christof Löding
Sarah Winter

References

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