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Characterization of Binary Constraint System Games

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Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8572))

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Abstract

We investigate a simple class of multi-prover interactive proof systems (classical non-local games), called binary constraint system (BCS) games, and characterize those that admit a perfect entangled strategy (i.e., a strategy with value 1 when the provers can use shared entanglement). Our characterization is in terms of a system of matrix equations. One application of this characterization is that, combined with a recent result of Arkhipov, it leads to a simple algorithm for determining whether certain restricted BCS games have a perfect entangled strategy, and, for the instances that do not, for bounding their value strictly below 1. An open question is whether, for the case of general BCS games, making this determination is computationally decidable. Our characterization might play a useful role in the resolution of this question.

Full version is available at http://arxiv.org/abs/1209.2729

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Author information

Authors and Affiliations

  1. Institute for Quantum Computing and School of Computer Science, University of Waterloo, Canada

    Richard Cleve

  2. Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, Canada

    Rajat Mittal

Authors
  1. Richard Cleve
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  2. Rajat Mittal
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Elias Koutsoupias

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Cleve, R., Mittal, R. (2014). Characterization of Binary Constraint System Games. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_27

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  • DOI: https://doi.org/10.1007/978-3-662-43948-7_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43947-0

  • Online ISBN: 978-3-662-43948-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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