Corpus ID: 160656

Algebraic Methods for Interactive Proof

@inproceedings{Lund2010AlgebraicMF,
  title={Algebraic Methods for Interactive Proof},
  author={S. Lund and Lance FortnowyHoward Karlo},
  year={2010}
}
Oracularization and Two-Prover One-Round Interactive Proofs against Nonlocal Strategies
TLDR
It is proved that exponentially small completeness-soundness gaps are best achievable unless soundness analysis uses the structure of the underlying system with unentangled provers, and it is NP-hard to approximate within an inverse-polynomial the value of a classical two-prover one-round game against entangled provers. Expand
On the Cryptographic Hardness of Local Search
TLDR
The core observation behind the results is that the unique proofs property of incrementally-verifiable computations previously used to demonstrate hardness in PLS can be traded with a simple incremental completeness property. Expand
Corrigendum to Affine Relativization
It has come to our attention that in Reference [2], Theorem 8, and its continuation, Theorem 10, are proven using an argument that contradicts a theorem of Löb [3] (see Reference [1, Theorem 1] forExpand
Affine Relativization
TLDR
This work defines what it means for any statement/proof to hold relative to any language, with no need to refer to devices like a Turing machine with an oracle tape, and dispels the widespread misconception that the notion of oracle access is inherently tied to a computational model. Expand
Quantum generalizations of the polynomial hierarchy with applications to QMA(2)
TLDR
This work studies whether two quantum generalizations of the polynomial-time hierarchy can similarly prove separations in the quantum setting, and places its third level into the Counting Hierarchy. Expand
Generalized Quantum Arthur-Merlin Games
TLDR
It is proved that the complexity class corresponding to two-turn quantum Arthur-Merlin games where both of the two messages are quantum, denoted qq-QAM in this paper, does not change by adding a constant number of turns of classical interaction prior to the communications of qq -QAM proof systems. Expand
Avoiding Simplicity is Complex
TLDR
Surprisingly, it is able to show unconditionally that avoiding simple strings (in the sense of KNt complexity) is difficult, and if E=NE, then accepting paths for nondeterministic exponential time machines can be found somewhat more quickly than the brute-force upper bound, if there are many accepting paths. Expand
General Properties of Quantum Zero-Knowledge Proofs
TLDR
All the four properties above hold also for the statistical zero-knowledge case and the first two properties hold even for the perfect zero- knowledge case, and it is proved that allowing a simulator to output "FAIL" does not change the power of quantum perfect zeroknowledge proofs. Expand
The Complexity Zoo
Two Query PCP with Sub-Constant Error
  • Dana Moshkovitz, R. Raz
  • Computer Science, Mathematics
  • 2008 49th Annual IEEE Symposium on Foundations of Computer Science
  • 2008
TLDR
This work shows that the NP-Complete language 3Sat has a PCPverifier that makes two queries to a proof of almost-linear size and achieves sub-constant probability of error o(1), and improves many of the hardness of approximation results that are proved using the parallel repetition theorem. Expand

References

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TLDR
A technique of arithmetization of the process of computation is introduced in order to obtain novel characterizations of certain complexity classes viamultivariate polynomials, demonstrating the applicability of this technique to classical complexity classes. Expand
Non-deterministic exponential time has two-prover interactive protocols
TLDR
It is shown that the class of languages having tow-prover interactive proof systems is nondeterministic exponential time and that to prove membership in languages inEXP, the honest provers need the power ofEXP only. Expand
Interactive Proof Systems and Alternating Time-Space Complexity
We show a rough equivalence between alternating time-space complexity and a public-coin interactive proof system with the veriier having a polynomial related time-space complexity. Special casesExpand
On the power of multiprover interactive protocols
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PSPACE is provable by two provers in one round
It is shown that every language in PSPACE, or equivalently every language accepted by an unbounded round interactive proof system, has a one-round, two-prover interactive proof with exponentiallyExpand
Designing programs that check their work
TLDR
This paper defines the concept of a program checker, designs program checkers for a few specific and carefully chosen problems in the class P of problems solvable in polynomial time and characterizes the problems that can be checked. Expand
On Completeness and Soundness in Interactive Proof Systems
TLDR
It is shown that any language having an interactive proof system has one (of the Arthur-Merlin type) with perfect completeness, and only languages in NP have interactive proofs with perfect soundness. Expand
Self - testing and self - correcting programs , with applications to numerical programs
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The Knowledge Complexity of Interactive Proof Systems
TLDR
A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. Expand
Are There Interactive Protocols for CO-NP Languages?
TLDR
Etude du probleme consistant a determiner quels types de langage peuvent traiter traiter des protocoles interactifs est toujours difficile de croissance. Expand
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