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Learning Definable Hypotheses on Trees

Authors Emilie Grienenberger, Martin Ritzert

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Author Details

Emilie Grienenberger
  • ENS Paris-Saclay, 61 Avenue du Président Wilson, 94230 Cachan, France
Martin Ritzert
  • RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany

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Emilie Grienenberger and Martin Ritzert. Learning Definable Hypotheses on Trees. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 24:1-24:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


We study the problem of learning properties of nodes in tree structures. Those properties are specified by logical formulas, such as formulas from first-order or monadic second-order logic. We think of the tree as a database encoding a large dataset and therefore aim for learning algorithms which depend at most sublinearly on the size of the tree. We present a learning algorithm for quantifier-free formulas where the running time only depends polynomially on the number of training examples, but not on the size of the background structure. By a previous result on strings we know that for general first-order or monadic second-order (MSO) formulas a sublinear running time cannot be achieved. However, we show that by building an index on the tree in a linear time preprocessing phase, we can achieve a learning algorithm for MSO formulas with a logarithmic learning phase.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • monadic second-order logic
  • trees
  • query learning


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