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DOI: 10.4230/LIPIcs.ICDT.2022.14

Inference of Shape Graphs for Graph Databases

Authors: Benoît Groz, Aurélien Lemay, Sławek Staworko, and Piotr Wieczorek

Published in: LIPIcs, Volume 220, 25th International Conference on Database Theory (ICDT 2022)

Abstract

We investigate the problem of constructing a shape graph that describes the structure of a given graph database. We employ the framework of grammatical inference, where the objective is to find an inference algorithm that is both sound, i.e., always producing a schema that validates the input graph, and complete, i.e., able to produce any schema, within a given class of schemas, provided that a sufficiently informative input graph is presented. We identify a number of fundamental limitations that preclude feasible inference. We present inference algorithms based on natural approaches that allow to infer schemas that we argue to be of practical importance.

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Benoît Groz, Aurélien Lemay, Sławek Staworko, and Piotr Wieczorek. Inference of Shape Graphs for Graph Databases. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{groz_et_al:LIPIcs.ICDT.2022.14,
  author =	{Groz, Beno\^{i}t and Lemay, Aur\'{e}lien and Staworko, S{\l}awek and Wieczorek, Piotr},
  title =	{{Inference of Shape Graphs for Graph Databases}},
  booktitle =	{25th International Conference on Database Theory (ICDT 2022)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-223-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{220},
  editor =	{Olteanu, Dan and Vortmeier, Nils},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.14},
  URN =		{urn:nbn:de:0030-drops-158889},
  doi =		{10.4230/LIPIcs.ICDT.2022.14},
  annote =	{Keywords: RDF, Schema, Inference, Learning, Fitting, Minimality, Containment}
}

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DOI: 10.4230/LIPIcs.MFCS.2020.38

Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead

Authors: Paul D. Gallot, Aurélien Lemay, and Sylvain Salvati

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract

We introduce the notion of high-order deterministic top-down tree transducers (HODT) whose outputs correspond to single-typed lambda-calculus formulas. These transducers are natural generalizations of known models of top-tree transducers such as: Deterministic Top-Down Tree Transducers, Macro Tree Transducers, Streaming Tree Transducers... We focus on the linear restriction of high order tree transducers with look-ahead (HODTR_lin), and prove this corresponds to tree to tree functional transformations defined by Monadic Second Order (MSO) logic. We give a specialized procedure for the composition of those transducers that uses a flow analysis based on coherence spaces and allows us to preserve the linearity of transducers. This procedure has a better complexity than classical algorithms for composition of other equivalent tree transducers, but raises the order of transducers. However, we also indicate that the order of a HODTR_lin can always be bounded by 3, and give a procedure that reduces the order of a HODTR_lin to 3. As those resulting HODTR_lin can then be transformed into other equivalent models, this gives an important insight on composition algorithm for other classes of transducers. Finally, we prove that those results partially translate to the case of almost linear HODTR: the class corresponds to the class of tree transformations performed by MSO with unfolding (not closed by composition), and provide a mechanism to reduce the order to 3 in this case.

Cite as

Paul D. Gallot, Aurélien Lemay, and Sylvain Salvati. Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 38:1-38:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gallot_et_al:LIPIcs.MFCS.2020.38,
  author =	{Gallot, Paul D. and Lemay, Aur\'{e}lien and Salvati, Sylvain},
  title =	{{Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{38:1--38:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.38},
  URN =		{urn:nbn:de:0030-drops-127050},
  doi =		{10.4230/LIPIcs.MFCS.2020.38},
  annote =	{Keywords: Transducers, \lambda-calculus, Trees}
}

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Documents authored by Lemay, Aurélien

Inference of Shape Graphs for Graph Databases

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Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead

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