Abstract
The parallel repetition theorem states that for any two provers one round game with value at most 1 − ε (for ε< 1/2), the value of the game repeated n times in parallel is at most (1 − ε 3)Ω(n/logs) where s is the size of the answers set [Raz98],[Hol07]. It is not known how the value of the game decreases when there are three or more players. In this paper we address the problem of the error decrease of parallel repetition game for k-provers where k > 2. We consider a special case of the No-Signaling model and show that the error of the parallel repetition of k provers one round game, for k > 2, in this model, decreases exponentially depending only on the error of the original game and on the number of repetitions. There were no prior results for k-provers parallel repetition for k > 2 in any model.
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References
Cai, J.-Y., Condon, A., Lipton, R.J.: On games of incomplete information. In: Choffrut, C., Lengauer, T. (eds.) STACS 1990. LNCS, vol. 415, Springer, Heidelberg (1990)
Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23(15), 880–884 (1969)
Cover, T.M., Thomas, J.A.: Elements of information theory, 2nd edn. Wiley-Interscience/John Wiley & Sons, Hoboken/ NJ (2006)
Feige, U.: On the success probability of the two provers in one-round proof systems. In: Structure in Complexity Theory Conference, pp. 116–123 (1991)
Feige, U., Kilian, J.: Two prover protocols: low error at affordable rates. In: Proceedings of the 26th Annual Symposium on the Theory of Computing, pp. 172–183. ACM Press, New York (May 1994)
Feige, U., Lovász, L.: Two-prover one-round proof systems: their power and their problems (extended abstract). In: STOC ’92: Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, pp. 733–744. ACM Press, New York (1992)
Fortnow, L.J.: Complexity - theoretic aspects of interactive proof systems. Technical Report MIT-LCS//MIT/LCS/TR-447, Department of Mathematics, Massachusetts Institute of Technology (1989)
Feige, U., Verbitsky, O.: Error reduction by parallel repetition—a negative result. Combinatorica 22(4), 461–478 (2002)
Feige, U., Verbitsky, O.: Error reduction by parallel repetition—a negative result. Combinatorica 22(4), 461–478 (2002)
Holenstein, T.: Parallel repetition: simplifications and the no-signaling case. In: STOC ’07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing (2007)
Popescu, S., Rohrlich, D.: Nonlocality as an axiom for quantum theory. In: Foundations of Physics, vol. 24(3), pp. 379–385 (1994)
Rao, A.: Parallel repetition in projection games and a concentration bound. In: STOC (2008)
Raz, R.: A parallel repetition theorem. SIAM J. Comput. 27(3), 763–803 (1998)
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Rosen, R. (2010). A K-Provers Parallel Repetition Theorem for a Version of No-Signaling Model. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_5
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DOI: https://doi.org/10.1007/978-3-642-14031-0_5
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