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MerlinArthur games and stoquastic complexity. Arxiv: quantph/0611021
, 2006
"... MA is a class of decision problems for which ‘yes’instances have a proof that can be efficiently checked by a classical randomized algorithm. We prove that MA has a natural complete problem which we call the stoquastic kSAT problem. This is a matrixvalued analogue of the satisfiability problem in ..."
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MA is a class of decision problems for which ‘yes’instances have a proof that can be efficiently checked by a classical randomized algorithm. We prove that MA has a natural complete problem which we call the stoquastic kSAT problem. This is a matrixvalued analogue of the satisfiability problem in which clauses are kqubit projectors with nonnegative matrix elements, while a satisfying assignment is a vector that belongs to the space spanned by these projectors. Stoquastic kSAT is the first nontrivial example of a MAcomplete problem. We also study the minimum eigenvalue problem for local stoquastic Hamiltonians that was introduced in Ref. [1], stoquastic LHMIN. A new complexity class StoqMA is introduced so that stoquastic LHMIN is StoqMAcomplete. We show that MA ⊆ StoqMA ⊆ SBP ∩QMA. Lastly, we consider the average LHMIN problem for local stoquastic Hamiltonians that depend on a random or ‘quenched disorder ’ parameter, stoquastic AVLHMIN. We prove that stoquastic AVLHMIN is contained in the complexity class AM, the class of decision problems for which yesinstances have a randomized interactive proof with twoway communication between prover and verifier.
Interactive and probabilistic proofchecking
 Annals of Pure and Applied Logic
, 2000
"... The notion of efficient proofchecking has always been central to complexity theory, and it gave rise to the definition of the class NP. In the last 15 years there has been a number of exciting, unexpected and deep developments in complexity theory that exploited the notion of randomized and interac ..."
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The notion of efficient proofchecking has always been central to complexity theory, and it gave rise to the definition of the class NP. In the last 15 years there has been a number of exciting, unexpected and deep developments in complexity theory that exploited the notion of randomized and interactive proofchecking. Results developed along this line of research have diverse and powerful applications in complexity theory, cryptography, and the theory of approximation algorithms for combinatorial optimization problems. In this paper we survey the main lines of developments in interactive and probabilistic proofchecking, with an emphasis on open questions.
Perfect ZeroKnowledge in Constant Rounds
, 1990
"... Quadratic residuosity and graph isomorphism are classic problems and the canonical examples of zeroknowledge languages. However, despite much research effort, all previous zeroknowledge proofs for them required either cryptography (and thus unproven assumptions) or an unbounded number of rounds of ..."
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Quadratic residuosity and graph isomorphism are classic problems and the canonical examples of zeroknowledge languages. However, despite much research effort, all previous zeroknowledge proofs for them required either cryptography (and thus unproven assumptions) or an unbounded number of rounds of message exchange. For both (and similar) languages, we exhibit zeroknowledge proofs that require 5 rounds and no unproven assumptions. Our solution is essentially optimal, in this setting, due to a recent lowerbound argument of Goldreich and Krawzcyk. 1 Introduction Interactive proofs and especially zeroknowledge ones have found many applications, most notably in the field of secure protocols. In all such proofs, interaction is the crucial resource, as prover and verifier exchange messages in rounds. The fundamental problem here is whether the number of rounds induces a hierarchy. That is, can we prove more languages in zero knowledge given more rounds? In a cryptographic setting the answ...
How To Withstand Mobile Virus Attacks
 In Proceedings of the tenth annual ACM symposium on Principles of distributed computing
, 1991
"... Rafail Ostrovsky Moti Yung y Abstract We initiate a study of distributed adversarial model of computation in which faults are nonstationary and can move through the network, analogous to a spread of a virus or a worm. We show how local computations (at each processor) and global computations c ..."
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Rafail Ostrovsky Moti Yung y Abstract We initiate a study of distributed adversarial model of computation in which faults are nonstationary and can move through the network, analogous to a spread of a virus or a worm. We show how local computations (at each processor) and global computations can be made robust using a constant factor resilience and a polynomial factor redundancy in the computation. 1 Introduction Computer viruses pose one of the central problems in distributed computing today. In this work, we initiate the study of "mobile viruses" (or computer network viruses)  intruders which try to compromise or destroy the system. Our machine model is a synchronous distributed architecture in which a malicious, infinitelypowerful adversary injects/distributes computer viruses at a certain rate at every round. We assume that the detection (of infected sites) can proceed with the same rate as the infection. We note that in practice, this is indeed a reasonable assumption t...
A Conceptual Framework for Specification, Analysis, and Design of Anonymity Services
"... Anonymity is an important issue in information security, which its main goal is to protect entities privacy in the systems. Different methods and protocols (with different types of anonymity services) have been developed so far to provide special anonymity requirements of applications. Each of these ..."
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Anonymity is an important issue in information security, which its main goal is to protect entities privacy in the systems. Different methods and protocols (with different types of anonymity services) have been developed so far to provide special anonymity requirements of applications. Each of these systems has been developed with different ad hoc approaches. In this paper we present a conceptual framework that makes specification, analysis and design of anonymity applications more systematic. To do this, first we go toward presenting a conceptual model of anonymity which can be used in clear description of different aspects of anonymity. Then we extract a list of anonymity primitives from the existing anonymity providing methods. These primitives are base functions which can be composed to form anonymity services to provide specified anonymity requirements of the system.