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The Proof of IP = PSPACE
, 2007
"... For a long time, the question of how a verifier can be convinced with high probability that a given theorem is provable without showing the whole proof, and of how rapidly this can be done, remained an open problem. This led interested parties to formulate and extensively study it in terms of intera ..."
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of interactive protocols. In 1992, Adi Shamir surprizingly completed the proof of IP = PSPACE, allowing IP to be placed in the standard classification of feasible computations [2]. This proof amazingly showed that when both randomization and interaction are allowed, the proofs that can be verified in polynomial
On IP=PSPACE and theorems with narrow proofs
 EATCS Bulletin
"... It has been shown that the class of languages with interactive proofs, IP, is exactly the class PSPACE. This surprising result elegantly places IP in the standard classification of feasible computations. Furthermore, the IP = PSPACE result reveals some very interesting and unsuspected properties of ..."
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Cited by 2 (1 self)
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It has been shown that the class of languages with interactive proofs, IP, is exactly the class PSPACE. This surprising result elegantly places IP in the standard classification of feasible computations. Furthermore, the IP = PSPACE result reveals some very interesting and unsuspected properties
On IP = PSPACE and Theorems with Narrow Proofs
, 1990
"... It has been shown that the class of languages with interactive proofs, IP, is exactly the class PSPACE. This surprising result elegantly places IP in the standard classification of feasible computations. Furthermore, the IP = PSPACE result reveals some very interesting and unsuspected properties of ..."
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It has been shown that the class of languages with interactive proofs, IP, is exactly the class PSPACE. This surprising result elegantly places IP in the standard classification of feasible computations. Furthermore, the IP = PSPACE result reveals some very interesting and unsuspected properties
Lecture 15,16: IP=PSPACE
"... 1. Since the prover can use an arbitrary function, it can in principle use unbounded computational power (or even compute undecidable functions). It is easy to see that given any verifier V, we can compute the optimum prover (which, given x, maximizes the verifiers acceptance probability) using poly ..."
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poly(x) space (and hence 2 poly(x) time).This is by enumerating each possible communication pattern and computing the probability of acceptance of verifier. Thus IP ⊆ P SP ACE. 2. As a motivating example we first prove #P ⊆ IP by giving an interactive protocol for #3SAT. i.e Given {φ, k
IP = PSPACE using Error Correcting Codes ∗
"... The IP theorem, which asserts that IP = PSPACE (Lund et. al., and Shamir, in J. ACM 39(4)), is one of the major achievements of complexity theory. The known proofs of the theorem are based on the arithmetization technique, which transforms a quantified Boolean formula into a related polynomial. The ..."
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The IP theorem, which asserts that IP = PSPACE (Lund et. al., and Shamir, in J. ACM 39(4)), is one of the major achievements of complexity theory. The known proofs of the theorem are based on the arithmetization technique, which transforms a quantified Boolean formula into a related polynomial
QIP = PSPACE
, 2010
"... We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update method to a class of semidefinite programs that captures the ..."
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Cited by 12 (2 self)
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the computational power of quantum interactive proofs. As the containment of PSPACE in QIP follows immediately from the wellknown equality IP = PSPACE, the equality QIP = PSPACE follows.
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 ..."
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Cited by 338 (28 self)
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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
The Relativized Relationship between Probabilistically Checkable Debate Systems, IP and PSPACE
, 1993
"... In 1990, PSPACE was shown to be identical to IP, the class of languages with interactive proofs [18, 20]. Recently, PSPACE was again recharacterized, this time in terms of (Random) Probabilistically Checkable Debate Systems [7, 8]. In particular, it was shown that PSPACE = PCDS[log n; 1] = RPCDS[lo ..."
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In 1990, PSPACE was shown to be identical to IP, the class of languages with interactive proofs [18, 20]. Recently, PSPACE was again recharacterized, this time in terms of (Random) Probabilistically Checkable Debate Systems [7, 8]. In particular, it was shown that PSPACE = PCDS[log n; 1] = RPCDS
Interactive Coding for Interactive Proofs
"... We consider interactive proof systems over adversarial communication channels. We show that the seminal result that IP = PSPACE still holds when the communication channel is malicious, allowing even a constant fraction of the communication to be arbitrarily corrupted. 1 ..."
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We consider interactive proof systems over adversarial communication channels. We show that the seminal result that IP = PSPACE still holds when the communication channel is malicious, allowing even a constant fraction of the communication to be arbitrarily corrupted. 1
Republic of Singapore
, 2009
"... We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelizedformofthematrixmultiplicativeweightsupdatemethodtoaclassofsemidefinite programs that captures the computationa ..."
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the computational power of quantum interactive proofs. As the containment of PSPACE in QIP follows immediately from the wellknown equality IP = PSPACE, the equality QIP = PSPACEfollows.
Results 1  10
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27