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• W2963811647 startingPage "17" @default.
• W2963811647 abstract "We present an efficient proof system for Multipoint Arithmetic Circuit Evaluation: for any arithmetic circuit C(x1, ..., xn) of size s and degree d over a field F, and any inputs a1, ..., aK ∈ Fn.the Prover sends the Verifier the values C(a1), ..., C(aK) ∈ F and a proof of O(K · d) length, andthe Verifier tosses poly(log(dK|F|/e)) coins and can check the proof in about O (K · (n+d)+s) time, with probability of error less than e.For small degree d, this proof system (a.k.a. MA-proof system) runs in nearly-linear time, and has many applications. For example, we obtain MA-proof systems that run in cn time (for various c < 2) for the Permanent, #Circuit-SAT for all sublinear-depth circuits, counting Hamiltonian cycles, and infeasibility of 0-1 linear programs. In general, the value of any polynomial in Valiant's class VNP can be certified faster than exhaustive summation over all possible assignments. These results strongly refute a Merlin-Arthur Strong ETH and Arthur-Merlin Strong ETH posed by Russell Impagliazzo and others.We also give a three-round (AMA) proof system for quantified Boolean formulas running in 22n/3+o(n) time, nearly-linear time MA-proof systems for counting orthogonal vectors in a collection and finding Closest Pairs in the Hamming metric, and a MA-proof system running in nk/2+O(1)-time for counting k-cliques in graphs.We point to some potential future directions for refuting the Nondeterministic Strong ETH." @default.
• W2963811647 created "2019-07-30" @default.
• W2963811647 creator A5052067562 @default.
• W2963811647 date "2016-05-29" @default.
• W2963811647 modified "2023-09-24" @default.
• W2963811647 title "Strong ETH breaks with Merlin and Arthur: short non-interactive proofs of batch evaluation" @default.
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• W2963811647 doi "https://doi.org/10.4230/lipics.ccc.2016.2" @default.
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