The parallel repetition of non-signaling games: counterexamples and dichotomy

Holmgren, Justin; Yang, Lili

doi:10.1145/3313276.3316367

Cited by 11 publications

(23 citation statements)

References 15 publications

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“…We mention that a related (yet weaker) theorem was proven in [15], where it was shown that given an MIP, one can distinguish between the case that its classical value is 1 (i.e., there exists a local strategy that is accepted with probability 1) and the case that its sub-non-signaling value is at most 1 − , in space poly( , 2 , 1/ ). This does not seem to be strong enough for us to use in order to obtain Theorem 1.1.…”

Section: Our Resultsmentioning

confidence: 99%

“…In the multi-prover regime, where the number of provers is greater than 2, we do not have a parallel repetition theorem. Moreover, in the non-signaling setting, Holmgren and Yang [15] provided a negative result, demonstrating that (in general) soundness cannot be amplified via parallel repetition.…”

Section: Our Resultsmentioning

confidence: 99%

“…Two relaxations of the notion of non-signaling were considered in the literature: the first is the notion of sub-non-signaling, by Lancien and Winter [24], and the second is the notion of honestreferee non-signaling by Holmgren and Yang [15]. In both cases these relaxed notions were motivated by the goal of proving a parallel repetition theorem for non-signaling strategies.…”

Section: Non-signaling Gamesmentioning

confidence: 99%

“…To this end, we use the notion of honest-referee non-signaling strategies, defined by Holmgren and Yang [15] (see Definition 3.5). Loosely speaking, given any sub-non-signaling strategy { } ∈Q that succeeds in convincing to accept with probability 1 − , we slightly modify the query distribution into a new distribution * that is obtained by restricting to a subset of its domain Q, such that and * are -close, for an arbitrary parameter > 0 of our choice.…”

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

“…We construct an honest-referee non-signaling strategy with respect to * that convinces to accept with probability at least 1 3 (1 − 2 / ). We then rely on a theorem from [15] that shows how to convert an honest-referee non-signaling strategy that succeeds in convincing with probability , into a non-signaling one that succeeds in convincing with probability ≥ 2 − ( 2 ) (see Theorem 5.1).…”

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

See 4 more Smart Citations

Non-signaling proofs with o(√ log n) provers are in PSPACE

Holden

Kalai

2020

Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

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Non-signaling proofs, motivated by quantum computation, have found applications in cryptography and hardness of approximation. An important open problem is characterizing the power of nonsignaling proofs. It is known that non-signaling proofs with two provers are characterized by PSPACE and that non-signaling proofs with poly()-provers are characterized by EXP. However, the power of-prover non-signaling proofs, for 2 < < poly() remained an open problem. We show that-prover non-signaling proofs (with negligible soundness) for = (log) are contained in PSPACE. We prove this via two different routes that are of independent interest. In both routes we consider a relaxation of non-signaling called subnon-signaling. Our main technical contribution (which is used in both our proofs) is a reduction showing how to convert any subnon-signaling strategy with value at least 1 − 2 −Ω (2) into a nonsignaling one with value at least 2 − (2). In the first route, we show that the classical prover reduction method for converting-prover games into 2-prover games carries over to the non-signaling setting with the following loss in soundness: if a-prover game has value less than 2 − 2 (for some constant > 0), then the corresponding 2-prover game has value less than 1 − 2 2 (for some constant > 0). In the second route we show that the value of a sub-non-signaling game can be approximated in space that is polynomial in the communication complexity and exponential in the number of provers. CCS CONCEPTS • Theory of computation → Interactive proof systems.

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Section: Our Resultsmentioning

confidence: 99%

Section: Our Resultsmentioning

confidence: 99%

Section: Non-signaling Gamesmentioning

confidence: 99%

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

See 3 more Smart Citations

Non-signaling proofs with o(√ log n) provers are in PSPACE

Holden

Kalai

2020

Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

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How Quantum Information Can Improve Social Welfare

Groisman

Gettrick

Mhalla

et al. 2020

IEEE J. Sel. Areas Inf. Theory

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How to Delegate Computations: The Power of No-Signaling Proofs

Tauman

RazRan

Rothblum

2021

J. ACM

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We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t = t ( n ), where the running time of the prover is poly ( t ) and the running time of the verifier is n · polylog ( t ). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. Our construction relies on the existence of a computational sub-exponentially secure private information retrieval ( PIR ) scheme. The proof exploits a curious connection between the problem of computation delegation and the model of multi-prover interactive proofs that are sound against no-signaling (cheating) strategies , a model that was studied in the context of multi-prover interactive proofs with provers that share quantum entanglement, and is motivated by the physical principle that information cannot travel faster than light. For any language computable in time t = t ( n ), we construct a multi-prover interactive proof ( MIP ), that is, sound against no-signaling strategies, where the running time of the provers is poly ( t ), the number of provers is polylog ( t ), and the running time of the verifier is n · polylog ( t ). In particular, this shows that the class of languages that have polynomial-time MIP s that are sound against no-signaling strategies, is exactly EXP . Previously, this class was only known to contain PSPACE . To convert our MIP into a 1-round delegation scheme, we use the method suggested by Aiello et al. (ICALP, 2000), which makes use of a PIR scheme. This method lacked a proof of security. We prove that this method is secure assuming the underlying MIP is secure against no-signaling provers.

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The parallel repetition of non-signaling games: counterexamples and dichotomy

Cited by 11 publications

References 15 publications

Non-signaling proofs with o(√ log n) provers are in PSPACE

Non-signaling proofs with o(√ log n) provers are in PSPACE

How Quantum Information Can Improve Social Welfare

How to Delegate Computations: The Power of No-Signaling Proofs

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