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58
Quantum ArthurMerlin games
 Computational Complexity
"... Abstract This paper studies quantum ArthurMerlin games, whichare a restricted form of quantum interactive proof system in which the verifier's messages are given by unbiased coinflips. The following results are proved. ffl For onemessage quantum ArthurMerlin games, whichcorrespond to the co ..."
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Cited by 71 (4 self)
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Abstract This paper studies quantum ArthurMerlin games, whichare a restricted form of quantum interactive proof system in which the verifier's messages are given by unbiased coinflips. The following results are proved. ffl For onemessage quantum ArthurMerlin games, whichcorrespond
Derandomizing ArthurMerlin Games
, 1998
"... We establish hardness versus randomness tradeoffs for ArthurMerlin games. We create efficient nondeterministic simulations of bounded round ArthurMerlin games, using a language in exponential time which small circuits cannot decide given access to an oracle for satisfiability. Our results yield s ..."
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Cited by 3 (1 self)
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We establish hardness versus randomness tradeoffs for ArthurMerlin games. We create efficient nondeterministic simulations of bounded round ArthurMerlin games, using a language in exponential time which small circuits cannot decide given access to an oracle for satisfiability. Our results yield
Generalized Quantum ArthurMerlin Games
"... Abstract This paper investigates the role of interaction and coins in quantum ArthurMerlin games (also called publiccoin quantum interactive proof systems). While the existing model restricts the messages from the verifier to be classical even in the quantum setting, the present work introduces a ..."
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Abstract This paper investigates the role of interaction and coins in quantum ArthurMerlin games (also called publiccoin quantum interactive proof systems). While the existing model restricts the messages from the verifier to be classical even in the quantum setting, the present work introduces
An efficient parallel repetition theorem for ArthurMerlin Games
 STOC'07
, 2007
"... We show a parallelrepetition theorem for constantround ArthurMerlin Games, using an efficient reduction. As a consequence, we show that parallel repetition reduces the soundnesserror at an optimal rate (up to a negligible factor) in constantround publiccoin argument systems, and constantround ..."
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Cited by 9 (2 self)
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We show a parallelrepetition theorem for constantround ArthurMerlin Games, using an efficient reduction. As a consequence, we show that parallel repetition reduces the soundnesserror at an optimal rate (up to a negligible factor) in constantround publiccoin argument systems, and constant
ArthurMerlin Games in Boolean Decision Trees
, 1997
"... It is well known that probabilistic boolean decision trees cannot be much more powerful than deterministic ones (N. Nisan, SIAM Journal on Computing, 20(6):9991007, 1991). Motivated by a question if randomization can significantly speed up a nondeterministic computation via a boolean decision tree ..."
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Cited by 2 (0 self)
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tree, we address structural properties of ArthurMerlin games in this model and prove some lower bounds. We consider two cases of interest, the first when the length of communication between the players is bounded and the second if it is not. While in the first case we can carry over the relations
ArthurMerlin Games in Boolean Decision Trees
"... Abstract It is well known that probabilistic boolean decision trees cannot be much more powerful than deterministic ones (N. Nisan, SIAM Journal on Computing, 20(6):9991007, 1991). Motivated by a question if randomization can significantly speed up a nondeterministic computation via a boolean decis ..."
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decision tree, we address structural properties of ArthurMerlin games in this model and prove some lower bounds. We consider two cases of interest, the first when the length of communication between the players is limited and the second if it is not. While in the first case we can carry over the relations
Derandomizing ArthurMerlin Games under Uniform Assumptions
 Computational Complexity
, 2000
"... We study how the nondeterminism versus determinism problem and the time versus space problem are related to the problem of derandomization. In particular, we show two ways of derandomizing the complexity class AM under uniform assumptions, which was only known previously under nonuniform assumption ..."
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Cited by 12 (0 self)
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We study how the nondeterminism versus determinism problem and the time versus space problem are related to the problem of derandomization. In particular, we show two ways of derandomizing the complexity class AM under uniform assumptions, which was only known previously under nonuniform assumptions [13, 14]. First, we prove that either AM = NP or it appears to any nondeterministic polynomial time adversary that NP is contained in deterministic subexponential time infinitely often. This implies that to any nondeterministic polynomial time adversary, the graph nonisomorphism problem appears to have subexponentialsize proofs infinitely often, the first nontrivial derandomization of this problem without any assumption. Next, we show that either all BPP = P, AM = NP, and PH P hold, or for any t(n) = 2 n) , DTIME(t(n)) DSPACE(t (n)) infinitely often for any constant > 0. Similar tradeoffs also hold for a whole range of parameters. This improves previous results [17, 5] ...
Random nondeterministic real functions and Arthur Merlin games
"... We construct a nondeterministic version of APP, denoted NAPP, which is the set of all real valued functions f : f0; 1g ! [0; 1], that are approximable within 1/k, by a probabilistic nondeterministic transducer, in time poly(1 ; n). We show that the subset of all Boolean functions in NAPP is ..."
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We construct a nondeterministic version of APP, denoted NAPP, which is the set of all real valued functions f : f0; 1g ! [0; 1], that are approximable within 1/k, by a probabilistic nondeterministic transducer, in time poly(1 ; n). We show that the subset of all Boolean functions in NAPP is exactly AM. We exhibit a natural complete problem for NAPP, namely computing the acceptance probability of a nondeterministic Boolean circuit. Then we prove that similarly to AM, the error probability for NAPP functions can be reduced exponentially. We also give a conondeterministic version, denoted coNAPP, and prove that all results for NAPP also hold for coNAPP. Then we construct two mappings between NAPP and promiseAM, which preserve completeness. Finally we show that in the world of deterministic computation, oracle access to AM is the same as oracle access to NAPP, i.e. P .
Results 1  10
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