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International Symposium on Foundations of Information and Knowledge Systems

FoIKS 2018: Foundations of Information and Knowledge Systems pp 303–321Cite as

Enumeration Complexity of Poor Man’s Propositional Dependence Logic

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10833))

Abstract

Dependence logics are a modern family of logics of independence and dependence which mimic notions of database theory. In this paper, we aim to initiate the study of enumeration complexity in the field of dependence logics and thereby get a new point of view on enumerating answers of database queries. Consequently, as a first step, we investigate the problem of enumerating all satisfying teams of formulas from a given fragment of propositional dependence logic. We distinguish between restricting the team size by arbitrary functions and the parametrised version where the parameter is the team size. We show that a polynomial delay can be reached for polynomials and otherwise in the parametrised setting we reach FPT delay. However, the constructed enumeration algorithm with polynomial delay requires exponential space. We show that an incremental polynomial delay algorithm exists which uses polynomial space only. Negatively, we show that for the general problem without restricting the team size, an enumeration algorithm running in polynomial space cannot exist.

This work was partially supported by DFG project ME4279/1-2.

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Acknowledgements

We thank the anonymous referees for their valuable comments.

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Authors and Affiliations

  1. Leibniz Universität Hannover, Institut für Theoretische Informatik, Appelstrasse 4, 30167, Hannover, Germany

    Arne Meier & Christian Reinbold

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  1. Arne Meier
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  2. Christian Reinbold
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Correspondence to Arne Meier .

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Editors and Affiliations

  1. Software Competence Center Hagenberg, Hagenberg im Mühlkreis, Austria

    Flavio Ferrarotti

  2. Vienna University of Technology, Vienna, Austria

    Stefan Woltran

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Meier, A., Reinbold, C. (2018). Enumeration Complexity of Poor Man’s Propositional Dependence Logic. In: Ferrarotti, F., Woltran, S. (eds) Foundations of Information and Knowledge Systems. FoIKS 2018. Lecture Notes in Computer Science(), vol 10833. Springer, Cham. https://doi.org/10.1007/978-3-319-90050-6_17

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  • DOI: https://doi.org/10.1007/978-3-319-90050-6_17

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