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Documents authored by Krötzsch, Markus

Document
DOI: 10.4230/LIPIcs.ICDT.2022.13
Tuple-Generating Dependencies Capture Complex Values

Authors: Maximilian Marx and Markus Krötzsch

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

Abstract
We formalise a variant of Datalog that allows complex values constructed by nesting elements of the input database in sets and tuples. We study its complexity and give a translation into sets of tuple-generating dependencies (TGDs) for which the standard chase terminates on any input database. We identify a fragment for which reasoning is tractable. As membership is undecidable for this fragment, we develop decidable sufficient conditions.
Cite as

Maximilian Marx and Markus Krötzsch. Tuple-Generating Dependencies Capture Complex Values. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{marx_et_al:LIPIcs.ICDT.2022.13,
  author =	{Marx, Maximilian and Kr\"{o}tzsch, Markus},
  title =	{{Tuple-Generating Dependencies Capture Complex Values}},
  booktitle =	{25th International Conference on Database Theory (ICDT 2022)},
  pages =	{13:1--13:20},
  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.2022.13},
  URN =		{urn:nbn:de:0030-drops-158876},
  doi =		{10.4230/LIPIcs.ICDT.2022.13},
  annote =	{Keywords: terminating standard chase, existential rules, Datalog, complexity}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICDT.2019.3
The Power of the Terminating Chase (Invited Talk)

Authors: Markus Krötzsch, Maximilian Marx, and Sebastian Rudolph

Published in: LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)

Abstract
The chase has become a staple of modern database theory with applications in data integration, query optimisation, data exchange, ontology-based query answering, and many other areas. Most application scenarios and implementations require the chase to terminate and produce a finite universal model, and a large arsenal of sufficient termination criteria is available to guarantee this (generally undecidable) condition. In this invited tutorial, we therefore ask about the expressive power of logical theories for which the chase terminates. Specifically, which database properties can be recognised by such theories, i.e., which Boolean queries can they realise? For the skolem (semi-oblivious) chase, and almost any known termination criterion, this expressivity is just that of plain Datalog. Surprisingly, this limitation of most prior research does not apply to the chase in general. Indeed, we show that standard - chase terminating theories can realise queries with data complexities ranging from PTime to non-elementary that are out of reach for the terminating skolem chase. A "Datalog-first" standard chase that prioritises applications of rules without existential quantifiers makes modelling simpler - and we conjecture: computationally more efficient. This is one of the many open questions raised by our insights, and we conclude with an outlook on the research opportunities in this area.
Cite as

Markus Krötzsch, Maximilian Marx, and Sebastian Rudolph. The Power of the Terminating Chase (Invited Talk). In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{krotzsch_et_al:LIPIcs.ICDT.2019.3,
  author =	{Kr\"{o}tzsch, Markus and Marx, Maximilian and Rudolph, Sebastian},
  title =	{{The Power of the Terminating Chase}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-101-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{127},
  editor =	{Barcelo, Pablo and Calautti, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.3},
  URN =		{urn:nbn:de:0030-drops-103057},
  doi =		{10.4230/LIPIcs.ICDT.2019.3},
  annote =	{Keywords: Existential rules, Tuple-generating dependencies, all-instances chase termination, expressive power, data complexity}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2018.12
Preserving Constraints with the Stable Chase

Authors: David Carral, Markus Krötzsch, Maximilian Marx, Ana Ozaki, and Sebastian Rudolph

Published in: LIPIcs, Volume 98, 21st International Conference on Database Theory (ICDT 2018)

Abstract
Conjunctive query answering over databases with constraints – also known as (tuple-generating) dependencies – is considered a central database task. To this end, several versions of a construction called chase have been described. Given a set Sigma of dependencies, it is interesting to ask which constraints not contained in Sigma that are initially satisfied in a given database instance are preserved when computing a chase over Sigma. Such constraints are an example for the more general class of incidental constraints, which when added to Sigma as new dependencies do not affect certain answers and might even speed up query answering. After formally introducing incidental constraints, we show that deciding incidentality is undecidable for tuple-generating dependencies, even in cases for which query entailment is decidable. For dependency sets with a finite universal model, the core chase can be used to decide incidentality. For the infinite case, we propose the stable chase, which generalises the core chase, and study its relation to incidental constraints.
Cite as

David Carral, Markus Krötzsch, Maximilian Marx, Ana Ozaki, and Sebastian Rudolph. Preserving Constraints with the Stable Chase. In 21st International Conference on Database Theory (ICDT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 98, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{carral_et_al:LIPIcs.ICDT.2018.12,
  author =	{Carral, David and Kr\"{o}tzsch, Markus and Marx, Maximilian and Ozaki, Ana and Rudolph, Sebastian},
  title =	{{Preserving Constraints with the Stable Chase}},
  booktitle =	{21st International Conference on Database Theory (ICDT 2018)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-063-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{98},
  editor =	{Kimelfeld, Benny and Amsterdamer, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2018.12},
  URN =		{urn:nbn:de:0030-drops-86015},
  doi =		{10.4230/LIPIcs.ICDT.2018.12},
  annote =	{Keywords: Incidental constraints, Tuple-generating dependencies, Infinite core chase, Universal Model, BCQ entailment}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.61
On the Complexity of Universality for Partially Ordered NFAs

Authors: Markus Krötzsch, Tomás Masopust, and Michaël Thomazo

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
Partially ordered nondeterminsitic finite automata (poNFAs) are NFAs whose transition relation induces a partial order on states, i.e., for which cycles occur only in the form of self-loops on a single state. A poNFA is universal if it accepts all words over its input alphabet. Deciding universality is \PSpace-complete for poNFAs, and we show that this remains true even when restricting to a fixed alphabet. This is nontrivial since standard encodings of alphabet symbols in, e.g., binary can turn self-loops into longer cycles. A lower coNP-complete complexity bound can be obtained if we require that all self-loops in the poNFA are deterministic, in the sense that the symbol read in the loop cannot occur in any other transition from that state. We find that such restricted poNFAs (rpoNFAs) characterise the class of R-trivial languages, and we establish the complexity of deciding if the language of an NFA is R-trivial. Nevertheless, the limitation to fixed alphabets turns out to be essential even in the restricted case: deciding universality of rpoNFAs with unbounded alphabets is PSPACE-complete. Our results also prove the complexity of the inclusion and equivalence problems, since universality provides the lower bound, while the upper bound is mostly known or proved in the paper.
Cite as

Markus Krötzsch, Tomás Masopust, and Michaël Thomazo. On the Complexity of Universality for Partially Ordered NFAs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 61:1-61:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{krotzsch_et_al:LIPIcs.MFCS.2016.61,
  author =	{Kr\"{o}tzsch, Markus and Masopust, Tom\'{a}s and Thomazo, Micha\"{e}l},
  title =	{{On the Complexity of Universality for Partially Ordered NFAs}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{61:1--61:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.61},
  URN =		{urn:nbn:de:0030-drops-64738},
  doi =		{10.4230/LIPIcs.MFCS.2016.61},
  annote =	{Keywords: automata, nondeterminism, partial order, universality}
}
Document
DOI: 10.4230/DagSemProc.08091.3
Approximate OWL Instance Retrieval with SCREECH

Authors: Pascal Hitzler, Markus Krötzsch, Sebastian Rudolph, and Tuvshintur Tserendorj

Published in: Dagstuhl Seminar Proceedings, Volume 8091, Logic and Probability for Scene Interpretation (2008)

Abstract
With the increasing interest in expressive ontologies for the Semantic Web, it is critical to develop scalable and efficient ontology reasoning techniques that can properly cope with very high data volumes. For certain application domains, approximate reasoning solutions, which trade soundness or completeness for increased reasoning speed, will help to deal with the high computational complexities which state of the art ontology reasoning tools have to face. In this paper, we present a comprehensive overview of the SCREECH approach to approximate instance retrieval with OWL ontologies, which is based on the KAON2 algorithms, facilitating a compilation of OWL DL TBoxes into Datalog, which is tractable in terms of data complexity. We present three different instantiations of the Screech approach, and report on experiments which show that the gain in efficiency outweighs the number of introduced mistakes in the reasoning process.
Cite as

Pascal Hitzler, Markus Krötzsch, Sebastian Rudolph, and Tuvshintur Tserendorj. Approximate OWL Instance Retrieval with SCREECH. In Logic and Probability for Scene Interpretation. Dagstuhl Seminar Proceedings, Volume 8091, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{hitzler_et_al:DagSemProc.08091.3,
  author =	{Hitzler, Pascal and Kr\"{o}tzsch, Markus and Rudolph, Sebastian and Tserendorj, Tuvshintur},
  title =	{{Approximate OWL Instance Retrieval with SCREECH}},
  booktitle =	{Logic and Probability for Scene Interpretation},
  pages =	{1--8},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8091},
  editor =	{Anthony G. Cohn and David C. Hogg and Ralf M\"{o}ller and Bernd Neumann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08091.3},
  URN =		{urn:nbn:de:0030-drops-16157},
  doi =		{10.4230/DagSemProc.08091.3},
  annote =	{Keywords: Description logics, automated reasoning, approximate reasoning, Horn logic}
}
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