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International Colloquium on Automata, Languages, and Programming

ICALP 2010: Automata, Languages and Programming pp 140–151Cite as

Polynomial-Space Approximation of No-Signaling Provers

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6198))

Abstract

In two-prover one-round interactive proof systems, no- signaling provers are those who are allowed to use arbitrary strategies, not limited to local operations, as long as their strategies cannot be used for communication between them. The study of multi-prover interactive proof systems with no-signaling provers has been motivated by the study of those with provers sharing quantum states. The relation between them is that no-signaling strategies include all the strategies realizable by provers sharing arbitrary entangled quantum states, and more. It was known that PSPACE ⊆ MIPns(2,1) ⊆ EXP, where MIPns(2,1) is the class of languages having a two-prover one-round interactive proof system with no-signaling provers.

This paper shows MIPns(2,1) = PSPACE. This is proved by constructing a fast parallel algorithm which approximates within an additive error the maximum winning probability of no-signaling players in a given cooperative two-player one-round game. The algorithm uses the fast parallel algorithm for the mixed packing and covering problem by Young (FOCS 2001).

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Author information

Authors and Affiliations

  1. Institute for Quantum Computing and School of Computer Science, University of Waterloo, 200 University Ave. W., Waterloo, ON, N2L 3G1, Canada

    Tsuyoshi Ito

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  1. Tsuyoshi Ito
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Editor information

Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Samson Abramsky

  2. Université de Bordeaux (LaBRI) & INRIA, 351, cours de la Libération, 33405, Talence Cedex, France

    Cyril Gavoille

  3. INRIA, Centre de Recherche Bordeaux – Sud-Ouest, 351 cours de la Libération, 33405, Talence Cedex, France

    Claude Kirchner

  4. Heinz Nixdorf Institute, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Friedhelm Meyer auf der Heide

  5. University of Patras and RACTI, 26500, Patras, Greece

    Paul G. Spirakis

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Ito, T. (2010). Polynomial-Space Approximation of No-Signaling Provers. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_13

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  • DOI: https://doi.org/10.1007/978-3-642-14165-2_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14164-5

  • Online ISBN: 978-3-642-14165-2

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