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DOI: 10.4230/LIPIcs.ICDT.2021.11

Answer Counting Under Guarded TGDs

Authors: Cristina Feier, Carsten Lutz, and Marcin Przybyłko

Published in: LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)

Abstract

We study the complexity of answer counting for ontology-mediated queries and for querying under constraints, considering conjunctive queries and unions thereof (UCQs) as the query language and guarded TGDs as the ontology and constraint language, respectively. Our main result is a classification according to whether answer counting is fixed-parameter tractable (FPT), W[1]-equivalent, #W[1]-equivalent, #W[2]-hard, or #A[2]-equivalent, lifting a recent classification for UCQs without ontologies and constraints due to Dell et al. [Holger Dell et al., 2019]. The classification pertains to various structural measures, namely treewidth, contract treewidth, starsize, and linked matching number. Our results rest on the assumption that the arity of relation symbols is bounded by a constant and, in the case of ontology-mediated querying, that all symbols from the ontology and query can occur in the data (so-called full data schema). We also study the meta-problems for the mentioned structural measures, that is, to decide whether a given ontology-mediated query or constraint-query specification is equivalent to one for which the structural measure is bounded.

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Cristina Feier, Carsten Lutz, and Marcin Przybyłko. Answer Counting Under Guarded TGDs. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{feier_et_al:LIPIcs.ICDT.2021.11,
  author =	{Feier, Cristina and Lutz, Carsten and Przyby{\l}ko, Marcin},
  title =	{{Answer Counting Under Guarded TGDs}},
  booktitle =	{24th International Conference on Database Theory (ICDT 2021)},
  pages =	{11:1--11:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-179-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{186},
  editor =	{Yi, Ke and Wei, Zhewei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.11},
  URN =		{urn:nbn:de:0030-drops-137195},
  doi =		{10.4230/LIPIcs.ICDT.2021.11},
  annote =	{Keywords: Ontology-Mediated Querying, Querying under Constraints, Answer Counting, Parameterized Complexity}
}

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Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2020.136

Computing Measures of Weak-MSO Definable Sets of Trees

Authors: Damian Niwiński, Marcin Przybyłko, and Michał Skrzypczak

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract

This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently definable in weak monadic second-order logic. The measure is the uniform coin-flipping measure or more generally it is generated by a branching stochastic process. The class of tree languages in consideration, although smaller than all regular tree languages, comprises in particular the languages definable in the alternation-free μ-calculus or in temporal logic CTL. Thus, the new algorithm may enhance the toolbox of probabilistic model checking.

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Damian Niwiński, Marcin Przybyłko, and Michał Skrzypczak. Computing Measures of Weak-MSO Definable Sets of Trees. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 136:1-136:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{niwinski_et_al:LIPIcs.ICALP.2020.136,
  author =	{Niwi\'{n}ski, Damian and Przyby{\l}ko, Marcin and Skrzypczak, Micha{\l}},
  title =	{{Computing Measures of Weak-MSO Definable Sets of Trees}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{136:1--136:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.136},
  URN =		{urn:nbn:de:0030-drops-125430},
  doi =		{10.4230/LIPIcs.ICALP.2020.136},
  annote =	{Keywords: infinite trees, weak alternating automata, coin-flipping measure}
}

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Answer Counting Under Guarded TGDs

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Computing Measures of Weak-MSO Definable Sets of Trees

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