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Document

**Published in:** LIPIcs, Volume 48, 19th International Conference on Database Theory (ICDT 2016)

Probabilistic programming languages are used for developing statistical models, and they typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. We propose and investigate an extension of Datalog for specifying statistical models, and establish a declarative probabilistic-programming paradigm over databases. Our proposed extension provides convenient mechanisms to include common numerical probability functions; in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program. Observations are naturally incorporated by means of integrity constraints over the extensional and intensional relations. The resulting semantics is robust under different chases and invariant to rewritings that preserve logical equivalence.

Vince Barany, Balder ten Cate, Benny Kimelfeld, Dan Olteanu, and Zografoula Vagena. Declarative Probabilistic Programming with Datalog. In 19th International Conference on Database Theory (ICDT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 48, pp. 7:1-7:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)

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@InProceedings{barany_et_al:LIPIcs.ICDT.2016.7, author = {Barany, Vince and ten Cate, Balder and Kimelfeld, Benny and Olteanu, Dan and Vagena, Zografoula}, title = {{Declarative Probabilistic Programming with Datalog}}, booktitle = {19th International Conference on Database Theory (ICDT 2016)}, pages = {7:1--7:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-002-6}, ISSN = {1868-8969}, year = {2016}, volume = {48}, editor = {Martens, Wim and Zeume, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2016.7}, URN = {urn:nbn:de:0030-drops-57761}, doi = {10.4230/LIPIcs.ICDT.2016.7}, annote = {Keywords: Chase, Datalog, probability measure space, probabilistic programming} }

Document

**Published in:** LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for XPath restricted to bounded depth documents with match width at most k is decidable; and that XPath is undecidable on any class of documents with unbounded braid width. We conjecture that these two parameters are equivalent, in the sense that a class of documents has bounded match width iff it has bounded braid width.

Vince Bárány, Mikolaj Bojanczyk, Diego Figueira, and Pawel Parys. Decidable classes of documents for XPath. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 99-111, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)

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@InProceedings{barany_et_al:LIPIcs.FSTTCS.2012.99, author = {B\'{a}r\'{a}ny, Vince and Bojanczyk, Mikolaj and Figueira, Diego and Parys, Pawel}, title = {{Decidable classes of documents for XPath}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, pages = {99--111}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2012}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.99}, URN = {urn:nbn:de:0030-drops-38512}, doi = {10.4230/LIPIcs.FSTTCS.2012.99}, annote = {Keywords: XPath, XML, class automata, data trees, data words, satisfiability} }

Document

**Published in:** LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

We investigate structures that can be represented by
omega-automata, so called omega-automatic structures, and prove
that relations defined over such structures in first-order logic
expanded by the first-order quantifiers `there exist at most
$aleph_0$ many', 'there exist finitely many' and 'there exist $k$
modulo $m$ many' are omega-regular. The proof identifies certain
algebraic properties of omega-semigroups.
As a consequence an omega-regular equivalence relation of countable
index has an omega-regular set of representatives. This implies
Blumensath's conjecture that a countable structure with an
$omega$-automatic presentation can be represented using automata
on finite words. This also complements a very recent result of
Hj"orth, Khoussainov, Montalban and Nies showing that there is an
omega-automatic structure which has no injective presentation.

Lukasz Kaiser, Sasha Rubin, and Vince Bárány. Cardinality and counting quantifiers on omega-automatic structures. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 385-396, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kaiser_et_al:LIPIcs.STACS.2008.1360, author = {Kaiser, Lukasz and Rubin, Sasha and B\'{a}r\'{a}ny, Vince}, title = {{Cardinality and counting quantifiers on omega-automatic structures}}, booktitle = {25th International Symposium on Theoretical Aspects of Computer Science}, pages = {385--396}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-06-4}, ISSN = {1868-8969}, year = {2008}, volume = {1}, editor = {Albers, Susanne and Weil, Pascal}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1360}, URN = {urn:nbn:de:0030-drops-13602}, doi = {10.4230/LIPIcs.STACS.2008.1360}, annote = {Keywords: \$omega\$-automatic presentations, \$omega\$-semigroups, \$omega\$-automata} }

Document

**Published in:** LIPIcs, Volume 48, 19th International Conference on Database Theory (ICDT 2016)

Probabilistic programming languages are used for developing statistical models, and they typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the probability space to a conditional subspace (the posterior). Use cases of such formalisms include the development of algorithms in machine learning and artificial intelligence. We propose and investigate an extension of Datalog for specifying statistical models, and establish a declarative probabilistic-programming paradigm over databases. Our proposed extension provides convenient mechanisms to include common numerical probability functions; in particular, conclusions of rules may contain values drawn from such functions. The semantics of a program is a probability distribution over the possible outcomes of the input database with respect to the program. Observations are naturally incorporated by means of integrity constraints over the extensional and intensional relations. The resulting semantics is robust under different chases and invariant to rewritings that preserve logical equivalence.

Vince Barany, Balder ten Cate, Benny Kimelfeld, Dan Olteanu, and Zografoula Vagena. Declarative Probabilistic Programming with Datalog. In 19th International Conference on Database Theory (ICDT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 48, pp. 7:1-7:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)

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@InProceedings{barany_et_al:LIPIcs.ICDT.2016.7, author = {Barany, Vince and ten Cate, Balder and Kimelfeld, Benny and Olteanu, Dan and Vagena, Zografoula}, title = {{Declarative Probabilistic Programming with Datalog}}, booktitle = {19th International Conference on Database Theory (ICDT 2016)}, pages = {7:1--7:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-002-6}, ISSN = {1868-8969}, year = {2016}, volume = {48}, editor = {Martens, Wim and Zeume, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2016.7}, URN = {urn:nbn:de:0030-drops-57761}, doi = {10.4230/LIPIcs.ICDT.2016.7}, annote = {Keywords: Chase, Datalog, probability measure space, probabilistic programming} }

Document

**Published in:** LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for XPath restricted to bounded depth documents with match width at most k is decidable; and that XPath is undecidable on any class of documents with unbounded braid width. We conjecture that these two parameters are equivalent, in the sense that a class of documents has bounded match width iff it has bounded braid width.

Vince Bárány, Mikolaj Bojanczyk, Diego Figueira, and Pawel Parys. Decidable classes of documents for XPath. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 99-111, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)

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@InProceedings{barany_et_al:LIPIcs.FSTTCS.2012.99, author = {B\'{a}r\'{a}ny, Vince and Bojanczyk, Mikolaj and Figueira, Diego and Parys, Pawel}, title = {{Decidable classes of documents for XPath}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, pages = {99--111}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2012}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.99}, URN = {urn:nbn:de:0030-drops-38512}, doi = {10.4230/LIPIcs.FSTTCS.2012.99}, annote = {Keywords: XPath, XML, class automata, data trees, data words, satisfiability} }

Document

**Published in:** LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

We investigate structures that can be represented by
omega-automata, so called omega-automatic structures, and prove
that relations defined over such structures in first-order logic
expanded by the first-order quantifiers `there exist at most
$aleph_0$ many', 'there exist finitely many' and 'there exist $k$
modulo $m$ many' are omega-regular. The proof identifies certain
algebraic properties of omega-semigroups.
As a consequence an omega-regular equivalence relation of countable
index has an omega-regular set of representatives. This implies
Blumensath's conjecture that a countable structure with an
$omega$-automatic presentation can be represented using automata
on finite words. This also complements a very recent result of
Hj"orth, Khoussainov, Montalban and Nies showing that there is an
omega-automatic structure which has no injective presentation.

Lukasz Kaiser, Sasha Rubin, and Vince Bárány. Cardinality and counting quantifiers on omega-automatic structures. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 385-396, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2008)

Copy BibTex To Clipboard

@InProceedings{kaiser_et_al:LIPIcs.STACS.2008.1360, author = {Kaiser, Lukasz and Rubin, Sasha and B\'{a}r\'{a}ny, Vince}, title = {{Cardinality and counting quantifiers on omega-automatic structures}}, booktitle = {25th International Symposium on Theoretical Aspects of Computer Science}, pages = {385--396}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-06-4}, ISSN = {1868-8969}, year = {2008}, volume = {1}, editor = {Albers, Susanne and Weil, Pascal}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1360}, URN = {urn:nbn:de:0030-drops-13602}, doi = {10.4230/LIPIcs.STACS.2008.1360}, annote = {Keywords: \$omega\$-automatic presentations, \$omega\$-semigroups, \$omega\$-automata} }

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