Derandomizing Arthur-Merlin Games under Uniform Assumptions

Lu, Chi-Jen

doi:10.1007/3-540-40996-3_26

Cited by 10 publications

(10 citation statements)

References 19 publications

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“…We soon explain our technique and the technical difficulty in this transition. The results of Lu (2001) and Impagliazzo et al (2002) are incomparable to ours and use different techniques. We would like to stress that our results give an analogue for AM of the derandomization result of Impagliazzo & Wigderson (1998), while previous results do not.…”

contrasting

confidence: 71%

“…Specifically, he showed that if NP ⊆ [io-pseudo(NP)]-DTIME(2 n ) for some > 0 then AM = NP. Impagliazzo et al (2002) were able to remove the [io-pseudo] quantifier from Lu (2001) and obtain the same conclusion using an assumption on exponential classes, namely, if NE ∩ coNE ⊆ [io]-DTIME(2 2 n ) for some > 0, then AM = NP.…”

mentioning

confidence: 84%

“…The problem we face now is how to find the "refuting" input x n ∈ {0, 1} n . As we explained earlier this exact problem appears in most uniform derandomization works (Impagliazzo & Wigderson 1998;Kabanets 2000;Lu 2001;Trevisan & Vadhan 2002). Previous works did not solve the problem, but rather weakened the result by requiring the derandomization to succeed in the pseudo-setting.…”

Section: Our Techniquementioning

confidence: 98%

“…• Using the easy witness method of Kabanets (2000), Lu (2001) showed a derandomization of AM under a uniform assumption. Specifically, he showed that if NP ⊆ [io-pseudo(NP)]-DTIME(2 n ) for some > 0 then AM = NP.…”

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confidence: 99%

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Uniform hardness versus randomness tradeoffs for Arthur-Merlin games

2003

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Abstract. Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap theorem" for BPP. We show an analogous result for AM: Either Arthur-Merlin protocols are very strong and everything in E = DTIME(2 O(n) ) can be proved to a subexponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm such that it is infeasible to come up with inputs on which the algorithm fails. We also show that if Arthur-Merlin protocols are not very strong (in the sense explained above) then AM ∩ coAM = NP ∩ coNP. Our technique combines the nonuniform hardness versus randomness tradeoff of Miltersen and Vinodchandran with "instance checking". A key ingredient in our proof is identifying a novel "resilience" property of hardness vs. randomness tradeoffs.

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confidence: 71%

mentioning

confidence: 84%

Section: Our Techniquementioning

confidence: 98%

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confidence: 99%

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Uniform hardness versus randomness tradeoffs for Arthur-Merlin games

2003

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“…Lu [Lu00] considers the modified generator Easy SAT : {0, 1} k → {0, 1} n that, on input y, outputs the truth table of the Boolean function computable by a SAT-oracle circuit whose description is y. If this modified generator can be uniformly broken almost everywhere, then we can guess, with zero error, a Boolean function of high SAT-oracle circuit complexity.…”

Section: Derandomizing Ammentioning

confidence: 99%

Derandomization: A Brief Overview

KABANETS¹

2004

Current Trends in Theoretical Computer Science

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Easiness Assumptions and Hardness Tests: Trading Time for Zero Error

Kabanets

2001

Journal of Computer and System Sciences

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We propose a new approach toward derandomization in the uniform setting, where it is computationally hard to find possible mistakes in the simulation of a given probabilistic algorithm. The approach consists in combining both easiness and hardness complexity assumptions: if a derandomization method based on an easiness assumption fails, then we obtain a certain hardness test that can be used to remove error in BPP algorithms. As an application, we prove that every RP algorithm can be simulated by a zeroerror probabilistic algorithm, running in expected subexponential time, that appears correct infinitely often (i.o.) to every efficient adversary. A similar result by Impagliazzo and Wigderson (FOCS'98) states that BPP allows deterministic subexponential-time simulations that appear correct with respect to any efficiently sampleable distribution i.o., under the assumption that EXP ] BPP; in contrast, our result does not rely on any unproven assumptions. As another application of our techniques, we get the following gap theorem for ZPP: either every RP algorithm can be simulated by a deterministic subexponential-time algorithm that appears correct i.o. to every efficient adversary or EXP=ZPP. In particular, this implies that if ZPP is somewhat easy, e.g., ZPP ı DTIME(2 n c ) for some fixed constant c, then RP is subexponentially easy in the uniform setting described above.

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Derandomizing Arthur-Merlin Games under Uniform Assumptions

Cited by 10 publications

References 19 publications

Uniform hardness versus randomness tradeoffs for Arthur-Merlin games

Uniform hardness versus randomness tradeoffs for Arthur-Merlin games

Derandomization: A Brief Overview

Easiness Assumptions and Hardness Tests: Trading Time for Zero Error

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