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Algebraic Methods for Interactive Proof Systems
, 1990
"... We present a new algebraic technique for the construction of interactive proof systems. We use our technique to prove that every language in the polynomialtime hierarchy has an interactive proof system. This technique played a pivotal role in the recent proofs that IP=PSPACE (Shamir) and that MIP ..."
Checking Computations in Polylogarithmic Time
, 1991
"... . Motivated by Manuel Blum's concept of instance checking, we consider new, very fast and generic mechanisms of checking computations. Our results exploit recent advances in interactive proof protocols [LFKN92], [Sha92], and especially the MIP = NEXP protocol from [BFL91]. We show that every no ..."
Abstract

Cited by 260 (10 self)
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. Motivated by Manuel Blum's concept of instance checking, we consider new, very fast and generic mechanisms of checking computations. Our results exploit recent advances in interactive proof protocols [LFKN92], [Sha92], and especially the MIP = NEXP protocol from [BFL91]. We show that every
Algebrization: A new barrier in complexity theory
 MIT Theory of Computing Colloquium
, 2007
"... Any proof of P � = NP will have to overcome two barriers: relativization and natural proofs. Yet over the last decade, we have seen circuit lower bounds (for example, that PP does not have linearsize circuits) that overcome both barriers simultaneously. So the question arises of whether there is a ..."
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Cited by 53 (3 self)
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—both inclusions such as IP = PSPACE and MIP = NEXP, and separations such as MAEXP � ⊂ P/poly —do indeed algebrize. Second, we show that almost all of the major open problems—including P versus NP, P versus RP, and NEXP versus P/poly—will require nonalgebrizing techniques. In some cases algebrization seems
Lecture 26
"... NEXP has multiprover interactive protocols If you’ve read the notes on the history of the PCP theorem referenced in Lecture 19 [3], you will already be familiar with the excitement that surrounded discoveries such as IP=PSPACE and NP=PCP(log, 1). Taken alone, however, these two theorems might seem ..."
Strong parallel repetition theorem for quantum XOR proof systems
 In Proceedings of the 22nd Annual Conference on Computational Complexity
, 2007
"... William Slofstra ∗ Sarvagya Upadhyay ∗ We consider a class of twoprover interactive proof systems where each prover returns a single bit to the verifier and the verifier’s verdict is a function of the XOR of the two bits received. Such proof systems, called XOR proof systems, have previously been s ..."
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Cited by 18 (0 self)
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shown to characterize MIP ( = NEXP) in the case of classical provers but to reside in EXP in the case of quantum provers (who are allowed to share a priori entanglement). We show that, in the quantum case, a perfect parallel repetition theorem holds for such proof systems in the following sense
unknown title
"... In this lecture, we will begin to talk about the “PCP Theorem ” (Probabilistically Checkable Proofs Theorem). Since the discovery of NPcompleteness in 1972, researchers had mulled over the issue of whether we can efficiently compute approximate solutions to NPhard optimization problems. They faile ..."
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verifier needs to do? We know that IP = PSPACE and MIP = NEXP [2] [3] [4], where MIP is akin to the class
Fast approximate PCPs
, 1999
"... We investigate the question of when a prover can aid a verifier to reliably compute a function faster than if the verifier were to compute the function on its own. Our focus is on the case when it is enough for the verifier to know that the answer is close to correct. The model of proof systems we ..."
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Cited by 5 (1 self)
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the existence of a large cut, a large matching, and a small bin packing. In contrast, the protocols used to show that IP = PSPACE; MIP = NEXP, and NP = PCP(lg n; 1) [Sha90, BFL91, ALM+98, BFLS90] require a verifier that runs in \Omega\Gamma n) time. In the process, we develop a set of tools for use
Generic separations
 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES
, 1996
"... We show that MAEXP, the exponential time version of problems in complexity theory. It is still true that virtually the MerlinArthur class, does not have polynomial size cir all of the theorems in computational complexity theory that cuits. This significantly improves the previous known result hav ..."
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theory that does not relativize. As a corollary to our viously always taken the form of collapses such as IP= separation result we also obtain that PEXP, the exponen PSPACE [LFKN92, Sha92], MIP=NEXP [BFL91] and tial time version of PP is not in P=poly. PCP(O(1);O(logn))=NP [ALM+92]. In this paper we
Entanglement in interactive proof systems with binary answers
 In Proceedings of STACS 2006
, 2006
"... If two classical provers share an entangled state, the resulting interactive proof system is significantly weakened [6]. We show that for the case where the verifier computes the XOR of two binary answers, the resulting proof system is in fact no more powerful than a system based on a single quantum ..."
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Cited by 17 (1 self)
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quantum prover: ⊕MIP ∗ [2] ⊆ QIP(2). This also implies that ⊕MIP ∗ [2] ⊆ EXP which was previously shown using a different method [7]. This contrasts with an interactive proof system where the two provers do not share entanglement. In that case, ⊕MIP[2] = NEXP for certain soundness and completeness
Quantum Multi Prover Interactive Proofs with Communicating Provers ∗
"... We introduce another variant of Quantum MIP, where the provers do not share entanglement, the communication between the verifier and the provers is quantum, but the provers are unlimited in the classical communication between them. At first, this model may seem very weak, as provers who exchange inf ..."
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We introduce another variant of Quantum MIP, where the provers do not share entanglement, the communication between the verifier and the provers is quantum, but the provers are unlimited in the classical communication between them. At first, this model may seem very weak, as provers who exchange
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