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

Authors Christof Löding, Sarah Winter



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Christof Löding
Sarah Winter

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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

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).
Keywords
  • tree transducers
  • tree automatic relation
  • uniformization

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