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58
On Small Space Complexity Classes Of Stochastic Turing Machines And ArthurMerlin Games
, 1997
"... A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types. Such devices are also called games against nature, ArthurMerlin games, or interactive proof systems with public coins. We investigate stochastic mac ..."
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A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types. Such devices are also called games against nature, ArthurMerlin games, or interactive proof systems with public coins. We investigate stochastic
Nondeterministic Circuit Lower Bounds from Mildly Derandomizing Arthurmerlin Games
, 2012
"... In several settings derandomization is known to follow from circuit lower bounds that themselves are equivalent to the existence of pseudorandom generators. This leaves open the question whether derandomization implies the circuit lower bounds that are known to imply it, i.e., whether the ability t ..."
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Cited by 2 (0 self)
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version of NP) with subpolynomial advice on infinitely many input lengths if and only if NEXP 6 ⊆ P/poly. We establish a full analogue in the setting of verification procedures: ArthurMerlin games can be simulated in Σ2SUBEXP (the subexponential version of Σ2P) with subpolynomial advice on infinitely
Uniform hardness vs. randomness tradeoffs for ArthurMerlin games
"... Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap result" for BPP. We show an analogous result for AM: Either ArthurMerlin protocols are very strong and everything in E = ) can be proved to a subexponential time verifier, or else ArthurMerlin protocols are weak an ..."
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Cited by 6 (0 self)
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Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap result" for BPP. We show an analogous result for AM: Either ArthurMerlin protocols are very strong and everything in E = ) can be proved to a subexponential time verifier, or else ArthurMerlin protocols are weak
Uniform Hardness Versus Randomness Tradeoffs For ArthurMerlin Games
"... ... A new ingredient in our proof is identifying a novel resiliency property of hardness vs. randomness tradeoffs. We observe that the MiltersenVinodchandran generator has this property. ..."
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Cited by 5 (3 self)
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... A new ingredient in our proof is identifying a novel resiliency property of hardness vs. randomness tradeoffs. We observe that the MiltersenVinodchandran generator has this property.
Adaptive Quantum Computation, Constant Depth Quantum Circuits and ArthurMerlin Games
, 2004
"... We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1 ..."
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We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1
Adaptive Quantum Computation, Constant Depth Quantum Circuits and ArthurMerlin Games
, 2004
"... We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1 ..."
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We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1
Adaptive Quantum Computation, Constant Depth Quantum Circuits and ArthurMerlin Games
, 2003
"... We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. We show that if an efficient ‘cou ..."
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We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. We show that if an efficient ‘counting ’ simulation, involving the calculation of conditional outcome probabilities, exists for these circuits then the classical polynomial hierarchy collapses. 1
Adaptive Quantum Computation, Constant Depth Quantum Circuits and ArthurMerlin Games
, 2004
"... We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1 ..."
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We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1
Computational Limitations of Stochastic Turing Machines and ArthurMerlin Games with Small Space Bounds
 IN PROC. 22. INT. SYMP
, 1997
"... A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types. Such devices are also called games against nature, ArthurMerlin games, or interactive proof systems with public coins. We give an overview on complexity ..."
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Cited by 1 (1 self)
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A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types. Such devices are also called games against nature, ArthurMerlin games, or interactive proof systems with public coins. We give an overview on complexity
Derandomizing ArthurMerlin games and approximate counting implies exponentialsize lower bounds
 In Proceedings of the IEEE Conference on Computational Complexity
, 2010
"... Abstract. We show that if ArthurMerlin protocols can be derandomized, then there is a language computable in deterministic exponentialtime with access to an NP oracle, that requires circuits of exponential size. More formally, if every promise problem in prAM, the class of promise problems that hav ..."
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Cited by 5 (0 self)
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Abstract. We show that if ArthurMerlin protocols can be derandomized, then there is a language computable in deterministic exponentialtime with access to an NP oracle, that requires circuits of exponential size. More formally, if every promise problem in prAM, the class of promise problems
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