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Documents authored by Thomazo, Michaël

Document
DOI: 10.4230/LIPIcs.ICDT.2019.18
A Single Approach to Decide Chase Termination on Linear Existential Rules

Authors: Michel Leclère, Marie-Laure Mugnier, Michaël Thomazo, and Federico Ulliana

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

Abstract
Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering. A knowledge base is then composed of an instance that contains incomplete data and a set of existential rules, and answers to queries are logically entailed from the knowledge base. This brought again to light the fundamental chase tool, and its different variants that have been proposed in the literature. It is well-known that the problem of determining, given a chase variant and a set of existential rules, whether the chase will halt on any instance, is undecidable. Hence, a crucial issue is whether it becomes decidable for known subclasses of existential rules. In this work, we consider linear existential rules with atomic head, a simple yet important subclass of existential rules that generalizes inclusion dependencies. We show the decidability of the all-instance chase termination problem on these rules for three main chase variants, namely semi-oblivious, restricted and core chase. To obtain these results, we introduce a novel approach based on so-called derivation trees and a single notion of forbidden pattern. Besides the theoretical interest of a unified approach and new proofs for the semi-oblivious and core chase variants, we provide the first positive decidability results concerning the termination of the restricted chase, proving that chase termination on linear existential rules with atomic head is decidable for both versions of the problem: Does every chase sequence terminate? Does some chase sequence terminate?
Cite as

Michel Leclère, Marie-Laure Mugnier, Michaël Thomazo, and Federico Ulliana. A Single Approach to Decide Chase Termination on Linear Existential Rules. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{leclere_et_al:LIPIcs.ICDT.2019.18,
  author =	{Lecl\`{e}re, Michel and Mugnier, Marie-Laure and Thomazo, Micha\"{e}l and Ulliana, Federico},
  title =	{{A Single Approach to Decide Chase Termination on Linear Existential Rules}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{18:1--18:19},
  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.2019.18},
  URN =		{urn:nbn:de:0030-drops-103200},
  doi =		{10.4230/LIPIcs.ICDT.2019.18},
  annote =	{Keywords: Chase, Tuple Generating Dependencies, Existential rules, Decidability}
}
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}
}
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