DROPS

Document

DOI: 10.4230/LIPIcs.ICDT.2025.24

Learning Tree Pattern Transformations

Authors: Daniel Neider, Leif Sabellek, Johannes Schmidt, Fabian Vehlken, and Thomas Zeume

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract

Explaining why and how a tree t structurally differs from another tree t^⋆ is a question that is encountered throughout computer science, including in understanding tree-structured data such as XML or JSON data. In this article, we explore how to learn explanations for structural differences between pairs of trees from sample data: suppose we are given a set {(t₁, t₁^⋆),… , (t_n, t_n^⋆)} of pairs of labelled, ordered trees; is there a small set of rules that explains the structural differences between all pairs (t_i, t_i^⋆)? This raises two research questions: (i) what is a good notion of "rule" in this context?; and (ii) how can sets of rules explaining a data set be learned algorithmically? We explore these questions from the perspective of database theory by (1) introducing a pattern-based specification language for tree transformations; (2) exploring the computational complexity of variants of the above algorithmic problem, e.g. showing NP-hardness for very restricted variants; and (3) discussing how to solve the problem for data from CS education research using SAT solvers.

Cite as

Daniel Neider, Leif Sabellek, Johannes Schmidt, Fabian Vehlken, and Thomas Zeume. Learning Tree Pattern Transformations. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{neider_et_al:LIPIcs.ICDT.2025.24,
  author =	{Neider, Daniel and Sabellek, Leif and Schmidt, Johannes and Vehlken, Fabian and Zeume, Thomas},
  title =	{{Learning Tree Pattern Transformations}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{24:1--24:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.24},
  URN =		{urn:nbn:de:0030-drops-229652},
  doi =		{10.4230/LIPIcs.ICDT.2025.24},
  annote =	{Keywords: Tree pattern transformations, learning from positive examples, computational complexity}
}

Document

DOI: 10.4230/LIPIcs.CSL.2013.615

The Complexity of Abduction for Equality Constraint Languages

Authors: Johannes Schmidt and Michał Wrona

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

Abstract

Abduction is a form of nonmonotonic reasoning that looks for an explanation for an observed manifestation according to some knowledge base. One form of the abduction problem studied in the literature is the propositional abduction problem parameterized by a structure \Gamma over the two-element domain. In that case, the knowledge base is a set of constraints over \Gamma, the manifestation and explanation are propositional formulas. In this paper, we follow a similar route. Yet, we consider abduction over infinite domain. We study the equality abduction problem parameterized by a relational first-order structure \Gamma over the natural numbers such that every relation in \Gamma is definable by a Boolean combination of equalities, a manifestation is a literal of the form (x = y) or (x != y), and an explanation is a set of such literals. Our main contribution is a complete complexity characterization of the equality abduction problem. We prove that depending on \Gamma, it is \Sigma^P_2-complete, or NP-complete, or in P.

Cite as

Johannes Schmidt and Michał Wrona. The Complexity of Abduction for Equality Constraint Languages. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 615-633, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@InProceedings{schmidt_et_al:LIPIcs.CSL.2013.615,
  author =	{Schmidt, Johannes and Wrona, Micha{\l}},
  title =	{{The Complexity of Abduction for Equality Constraint Languages}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{615--633},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.615},
  URN =		{urn:nbn:de:0030-drops-42229},
  doi =		{10.4230/LIPIcs.CSL.2013.615},
  annote =	{Keywords: Abduction, infinite structures, equality constraint languages, computational complexity, algebraic approach}
}

Search Results

Documents authored by Schmidt, Johannes

Learning Tree Pattern Transformations

Abstract

Cite as

The Complexity of Abduction for Equality Constraint Languages

Abstract

Cite as

Thanks for your feedback!

Could not send message