Succinct delegation for low-space non-deterministic computation

Badrinarayanan, Saikrishna; Kalai, Yael Tauman; Khurana, Dakshita; Sahai, Amit; Wichs, Daniel

doi:10.1145/3188745.3188924

Cited by 25 publications

(19 citation statements)

References 20 publications

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“…More recently, Kalai, Raz and Rothblum [22] showed that there exists a poly( )-prover NS MIP for EXP, thus characterizing the power of -prover NS MIP for = poly( ). 2 These works left open the following question: What is the power of -prover NS MIP for 2 < < poly( )? This question was studied by Chiesa, Manohar and Shinkar in [7], who constructed a -prover NS MIP for EXP with = (1), albeit where the verifier's queries are of exponential length.…”

Section: Prior Workmentioning

confidence: 99%

“…However, it reduces the total probability of Sim (1) [ ], , yet we argue that it does not reduce the probability by too much, and that indeed Equation (3) holds. (2) Step 2. We convert the family of distributions {Sim (1) , } into a family of honest-referee non-signaling distributions.…”

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

“…(a) Step 2(a). We modify {Sim (1) , } to a new family of distributions {Sim (2) , } that still satisfies Equation 2, yet in addition for every and the probability that Sim…”

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

“…outputs ⊥ depends only on | |, and is otherwise independent of and . We define Sim (2) , by lowering the probability mass of Sim (1) , . However, to ensure that we do not lower the probability mass by too much, we need to focus only on queries such that the probability that Sim From now on we focus only on ∈ GOOD.…”

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

“…In [22], the same authors constructed an MIP that is secure against non-signaling attacks for every language in EXP, thus yielding the first one-round delegation scheme for all deterministic computations, under standard cryptographic assumptions. This application of non-signaling to computation delegation has proved to be very fruitful, and yielded numerous followup works (e.g., [2,5,18,19]). Moreover, all one-round delegation schemes in the literature that are based on standard cryptographic assumptions use the concept of non-signaling.…”

Section: Introductionmentioning

confidence: 99%

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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: Prior Workmentioning

confidence: 99%

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

“…(a) Step 2(a). We modify {Sim (1) , } to a new family of distributions {Sim (2) , } that still satisfies Equation 2, yet in addition for every and the probability that Sim…”

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

Section: Overview Of the Proof Of Theorem 42mentioning

confidence: 99%

Section: Introductionmentioning

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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No-signaling Linear PCPs

Kiyoshima¹

2018

Theory of Cryptography

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Outsourcing Computation: The Minimal Refereed Mechanism

Kong

Peikert

Schoenebeck

et al. 2019

Web and Internet Economics

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We consider a setting where a verifier with limited computation power delegates a resource intensive computation task-which requires a T ×S computation tableau-to two provers where the provers are rational in that each prover maximizes their own payoff-taking into account losses incurred by the cost of computation. We design a mechanism called the Minimal Refereed Mechanism (MRM) such that if the verifier has O(log S + log T ) time and O(log S + log T ) space computation power, then both provers will provide a honest result without the verifier putting any effort to verify the results. The amount of computation required for the provers (and thus the cost) is a multiplicative log S-factor more than the computation itself, making this schema efficient especially for low-space computations.

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Succinct delegation for low-space non-deterministic computation

Cited by 25 publications

References 20 publications

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

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

No-signaling Linear PCPs

Outsourcing Computation: The Minimal Refereed Mechanism

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