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

DOI: 10.4230/LIPIcs.ICALP.2020.106

Decision Problems in Information Theory

Authors: Mahmoud Abo Khamis, Phokion G. Kolaitis, Hung Q. Ngo, and Dan Suciu

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

Abstract

Constraints on entropies are considered to be the laws of information theory. Even though the pursuit of their discovery has been a central theme of research in information theory, the algorithmic aspects of constraints on entropies remain largely unexplored. Here, we initiate an investigation of decision problems about constraints on entropies by placing several different such problems into levels of the arithmetical hierarchy. We establish the following results on checking the validity over all almost-entropic functions: first, validity of a Boolean information constraint arising from a monotone Boolean formula is co-recursively enumerable; second, validity of "tight" conditional information constraints is in Π⁰₃. Furthermore, under some restrictions, validity of conditional information constraints "with slack" is in Σ⁰₂, and validity of information inequality constraints involving max is Turing equivalent to validity of information inequality constraints (with no max involved). We also prove that the classical implication problem for conditional independence statements is co-recursively enumerable.

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Mahmoud Abo Khamis, Phokion G. Kolaitis, Hung Q. Ngo, and Dan Suciu. Decision Problems in Information Theory. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 106:1-106:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{abokhamis_et_al:LIPIcs.ICALP.2020.106,
  author =	{Abo Khamis, Mahmoud and Kolaitis, Phokion G. and Ngo, Hung Q. and Suciu, Dan},
  title =	{{Decision Problems in Information Theory}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{106:1--106:20},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.106},
  URN =		{urn:nbn:de:0030-drops-125137},
  doi =		{10.4230/LIPIcs.ICALP.2020.106},
  annote =	{Keywords: Information theory, decision problems, arithmetical hierarchy, entropic functions}
}

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DOI: 10.4230/LIPIcs.ICDT.2019.21

Boolean Tensor Decomposition for Conjunctive Queries with Negation

Authors: Mahmoud Abo Khamis, Hung Q. Ngo, Dan Olteanu, and Dan Suciu

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

Abstract

We propose an approach for answering conjunctive queries with negation, where the negated relations have bounded degree. Its data complexity matches that of the InsideOut and PANDA algorithms for the positive subquery of the input query and is expressed in terms of the fractional hypertree width and the submodular width respectively. Its query complexity depends on the structure of the conjunction of negated relations; in general it is exponential in the number of join variables occurring in negated relations yet it becomes polynomial for several classes of queries. This approach relies on several contributions. We show how to rewrite queries with negation on bounded-degree relations into equivalent conjunctive queries with not-all-equal (NAE) predicates, which are a multi-dimensional analog of disequality (!=). We then generalize the known color-coding technique to conjunctions of NAE predicates and explain it via a Boolean tensor decomposition of conjunctions of NAE predicates. This decomposition can be achieved via a probabilistic construction that can be derandomized efficiently.

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Mahmoud Abo Khamis, Hung Q. Ngo, Dan Olteanu, and Dan Suciu. Boolean Tensor Decomposition for Conjunctive Queries with Negation. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{abokhamis_et_al:LIPIcs.ICDT.2019.21,
  author =	{Abo Khamis, Mahmoud and Ngo, Hung Q. and Olteanu, Dan and Suciu, Dan},
  title =	{{Boolean Tensor Decomposition for Conjunctive Queries with Negation}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{21:1--21:19},
  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.2019.21},
  URN =		{urn:nbn:de:0030-drops-103236},
  doi =		{10.4230/LIPIcs.ICDT.2019.21},
  annote =	{Keywords: color-coding, combined complexity, negation, query evaluation}
}

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Documents authored by Abo Khamis, Mahmoud

Decision Problems in Information Theory

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Boolean Tensor Decomposition for Conjunctive Queries with Negation

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