Streaming Verification in Data Analysis

Daruki, Samira; Thaler, Justin; Venkatasubramanian, Suresh

doi:10.1007/978-3-662-48971-0_60

Cited by 5 publications

(7 citation statements)

References 26 publications

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“…These protocols have been studied by many ever since; see, for example, [15,16,38,39,44,45]. Recently, interactive proofs have also been studied in streaming settings [17,21,22,23].…”

Section: Related Workmentioning

confidence: 99%

Rational Proofs with Multiple Provers

Chen

McCauley

Singh

2016

Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

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Interactive proofs (IP) model a world where a verifier delegates computation to an untrustworthy prover, verifying the prover's claims before accepting them. IP protocols have applications in areas such as verifiable computation outsourcing, computation delegation, cloud computing, etc. In these applications, the verifier may pay the prover based on the quality of his work. Rational interactive proofs (RIP), introduced by Azar and Micali (2012), are an interactive-proof system with payments, in which the prover is rational rather than untrustworthy-he may lie, but only to increase his payment. Rational proofs leverage the prover's rationality to obtain simple and efficient protocols. Azar and Micali show that RIP=IP(=PSPACE), i.e., the set of provable languages stay the same with a single rational prover (compared to classic IP). They leave the question of whether multiple provers are more powerful than a single prover for rational and classical proofs as an open problem.In this paper we introduce multi-prover rational interactive proofs (MRIP). Here, a verifier cross-checks the provers' answers with each other and pays them according to the messages exchanged. The provers are cooperative and maximize their total expected payment if and only if the verifier learns the correct answer to the problem. We further refine the model of MRIP to incorporate utility gaps, which is the loss in payment suffered by provers who mislead the verifier to the wrong answer.We define the class of MRIP protocols with constant, noticeable and negligible utility gaps-the payment loss due to a wrong answer is O(1), 1/n O(1) and 1/2 n O(1) respectively, where n is the length of the input. We give tight characterization for all three MRIP classes. On the way, we resolve Azar and Micali's open problem-under standard complexity-theoretic assumptions, MRIP is not only more powerful than RIP, but also more powerful than MIP (classic multi-prover IP); and this is true even the utility gap is required to be constant. We further show that the full power of each MRIP class can be achieved using only two provers and three rounds of communication.

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“…These protocols have been studied by many ever since; see, for example, [15,16,38,39,44,45]. Recently, interactive proofs have also been studied in streaming settings [17,21,22,23].…”

Section: Related Workmentioning

confidence: 99%

Rational Proofs with Multiple Provers

Chen

McCauley

Singh

2016

Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

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“…Subsequent Work. Subsequent to the conference version of this paper, Daruki et al [18] gave SIPs for a number of problems in computational geometry and data analysis. In two of their results, they built on our work to give a 2-message SIP of polylogarithmic cost for the Minimum Enclosing Ball problem, and a 3-message SIP of polylogarithmic cost for computing a 2-approximation to the k-center in a metric space.…”

Section: Related Workmentioning

confidence: 99%

Verifiable Stream Computation and Arthur--Merlin Communication

Chakrabarti¹,

Cormode²,

McGregor³

et al. 2019

SIAM J. Comput.

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In the setting of streaming interactive proofs (SIPs), a client (verifier) needs to compute a given function on a massive stream of data, arriving online, but is unable to store even a small fraction of the data. It outsources the processing to a third party service (prover), but is unwilling to blindly trust answers returned by this service. Thus, the service cannot simply supply the desired answer; it must convince the verifier of its correctness via a short interaction after the stream has been seen. In this work we study "barely interactive" SIPs. Specifically, we show that one or two rounds of interaction suffice to solve several query problems-including Index, Median, Nearest Neighbor Search, Pattern Matching, and Range Counting-with polylogarithmic space and communication costs. Such efficiency with O(1) rounds of interaction was thought to be impossible based on previous work. On the other hand, we initiate a formal study of the limitations of constant-round SIPs by introducing a new hierarchy of communication models called Online Interactive Proofs (OIPs). The online nature of these models is analogous to the streaming restriction placed upon the verifier in a SIP. We give upper and lower bounds that (1) characterize, up to quadratic blowups, every finite level of the OIP hierarchy in terms of other well-known communication complexity classes, (2) separate the first four levels of the hierarchy, and (3) reveal that the hierarchy collapses to the fourth level. Our study of OIPs reveals marked contrasts and some parallels with the classic Turing Machine theory of interactive proofs, establishes limits on the power of existing techniques for developing constantround SIPs, and provides a new characterization of (non-online) Arthur-Merlin communication in terms of an online model.

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“…In a recent line of research, the data stream model was extended to support several interactive and non-interactive proof systems. The model of streaming algorithms with non-interactive proofs was first introduced in (Chakrabarti et al 2014b) and extended in (Chakrabarti et al 2014a(Chakrabarti et al , 2015Cormode et al 2012Cormode et al , 2013Daruki et al 2015;Gur & Raz 2013;Thaler 2014). We remark that there are several related notions between MAPs and annotated data streams.…”

Section: Parameterized Concatenation Problems Our Techniques Formentioning

confidence: 99%

Non-interactive proofs of proximity

Gur

Rothblum

2016

comput. complex.

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We initiate a study of non-interactive proofs of proximity. These proof systems consist of a verifier that wishes to ascertain the validity of a given statement, using a short (sublinear length) explicitly given proof, and a sublinear number of queries to its input. Since the verifier cannot even read the entire input, we only require it to reject inputs that are far from being valid. Thus, the verifier is only assured of the proximity of the statement to a correct one. Such proof systems can be viewed as the N P (or more accurately MA) analogue of property testing. We explore both the power and limitations of non-interactive proofs of proximity. We show that such proof systems can be exponentially stronger than property testers, but are exponentially weaker than the interactive proofs of proximity studied by Rothblum, Vadhan and Wigderson (STOC 2013). In addition, we show a natural problem that has a full and (almost) tight multiplicative trade-off between the length of the proof and the verifier's query complexity. On the negative side, we also show that there exist properties for which even a linearly long (noninteractive) proof of proximity cannot significantly reduce the query complexity.

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Streaming Verification in Data Analysis

Cited by 5 publications

References 26 publications

Rational Proofs with Multiple Provers

Rational Proofs with Multiple Provers

Verifiable Stream Computation and Arthur--Merlin Communication

Non-interactive proofs of proximity

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