4 Search Results for "Hannula, Miika"

Document
DOI: 10.4230/LIPIcs.CSL.2021.27
On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic

Authors: Miika Hannula, Juha Kontinen, Martin Lück, and Jonni Virtema

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Abstract
Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to term constructions, 2) restrictions to the form of the Boolean matrix. Of the first sort, we consider two kinds of restrictions: firstly, disallowing nested use of proper function variables, and secondly stipulating that each function variable must appear with a fixed sequence of arguments. Of the second sort, we consider Horn, Krom, and core fragments of the Boolean matrix. We classify the complexity of logics obtained by combining these two types of restrictions. We show that, in most cases, logics with k alternating blocks of function quantifiers are complete for the kth or (k-1)th level of the exponential time hierarchy. Furthermore, we establish NL-completeness for the Krom and core fragments, when k = 1 and both restrictions of the first sort are in effect.
Cite as

Miika Hannula, Juha Kontinen, Martin Lück, and Jonni Virtema. On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 27:1-27:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hannula_et_al:LIPIcs.CSL.2021.27,
  author =	{Hannula, Miika and Kontinen, Juha and L\"{u}ck, Martin and Virtema, Jonni},
  title =	{{On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{27:1--27:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.27},
  URN =		{urn:nbn:de:0030-drops-134610},
  doi =		{10.4230/LIPIcs.CSL.2021.27},
  annote =	{Keywords: quantified Boolean formulae, computational complexity, second-order logic, Horn and Krom fragment}
}
Document
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.
Cite as

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}
}
Document
DOI: 10.4230/LIPIcs.CSL.2017.28
Validity and Entailment in Modal and Propositional Dependence Logics

Authors: Miika Hannula

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract
The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal dependence logic. Thus far, however, the validity and entailment properties of these logics have remained uncharacterised to a great extent. This paper establishes a complete classification of the complexity of validity and entailment in modal and propositional dependence logics. In particular, we address the question of the complexity of validity in modal dependence logic. By showing that it is NEXPTIME-complete we refute an earlier conjecture proposing a higher complexity for the problem.
Cite as

Miika Hannula. Validity and Entailment in Modal and Propositional Dependence Logics. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 28:1-28:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{hannula:LIPIcs.CSL.2017.28,
  author =	{Hannula, Miika},
  title =	{{Validity and Entailment in Modal and Propositional Dependence Logics}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.28},
  URN =		{urn:nbn:de:0030-drops-76691},
  doi =		{10.4230/LIPIcs.CSL.2017.28},
  annote =	{Keywords: modal logic, propositional logic, dependence logic, entailment, validity, complexity}
}
Document
DOI: 10.4230/LIPIcs.CSL.2013.263
Hierarchies in independence logic

Authors: Pietro Galliani, Miika Hannula, and Juha Kontinen

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

Abstract
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax semantics for these logics, we relate these fragments of inclusion and independence logic to familiar sublogics of existential second-order logic. We also show that, with respect to the stronger strict semantics, inclusion logic is equivalent to existential second-order logic.
Cite as

Pietro Galliani, Miika Hannula, and Juha Kontinen. Hierarchies in independence logic. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 263-280, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@InProceedings{galliani_et_al:LIPIcs.CSL.2013.263,
  author =	{Galliani, Pietro and Hannula, Miika and Kontinen, Juha},
  title =	{{Hierarchies in independence logic}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{263--280},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.263},
  URN =		{urn:nbn:de:0030-drops-42021},
  doi =		{10.4230/LIPIcs.CSL.2013.263},
  annote =	{Keywords: Existential second-order logic, Independence logic, Inclusion logic, Expressiveness hierarchies}
}
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