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Hardness of Network Satisfaction for Relation Algebras with Normal Representations

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Relational and Algebraic Methods in Computer Science (RAMiCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12062))

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Abstract

We study the computational complexity of the general network satisfaction problem for a finite relation algebra A with a normal representation B. If B contains a non-trivial equivalence relation with a finite number of equivalence classes, then the network satisfaction problem for A is NP-hard. As a second result, we prove hardness if B has domain size at least three and contains no non-trivial equivalence relations but a symmetric atom a with a forbidden triple (a, a, a), that is, \(a \not \le a \circ a\). We illustrate how to apply our conditions on two small relation algebras.

M. Bodirsky—The author has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 681988, CSP-Infinity).

S. Knäuer—The author is supported by DFG Graduiertenkolleg 1763 (QuantLA).

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Authors and Affiliations

  1. Institut für Algebra, TU Dresden, 01062, Dresden, Germany

    Manuel Bodirsky & Simon Knäuer

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  1. Manuel Bodirsky
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  2. Simon Knäuer
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Correspondence to Simon Knäuer .

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Editors and Affiliations

  1. Laboratoire d’informatique (LIX), École Polytechnique, Palaiseau, France

    Uli Fahrenberg

  2. Faculty of Mathematics, Chapman University, Orange, CA, USA

    Peter Jipsen

  3. Department of Computer Science, Brock University, St. Catharines, ON, Canada

    Michael Winter

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Bodirsky, M., Knäuer, S. (2020). Hardness of Network Satisfaction for Relation Algebras with Normal Representations. In: Fahrenberg, U., Jipsen, P., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2020. Lecture Notes in Computer Science(), vol 12062. Springer, Cham. https://doi.org/10.1007/978-3-030-43520-2_3

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  • DOI: https://doi.org/10.1007/978-3-030-43520-2_3

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  • Online ISBN: 978-3-030-43520-2

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