Algebraic methods for interactive proof systems

@article{Lund1992AlgebraicMF,
  title={Algebraic methods for interactive proof systems},
  author={Carsten Lund and Lance Fortnow and Howard J. Karloff and Noam Nisan},
  journal={J. ACM},
  year={1992},
  volume={39},
  pages={859-868}
}
A new algebraic technique for the construction of interactive proof systems is presented. Our technique is used to prove that every language in the polynomial-time hierarchy has an interactive proof system. This technique played a pivotal role in the recent proofs that IP = PSPACE [28] and that MIP = NEXP [4]. 
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  • Theor. Comput. Sci.
  • 2003
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  • Mathematics, Computer Science
  • 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
  • 1999
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This model, developed by Ben-Or et al. (1988) allows the verifier to play the provers off each other, is shown equivalent to an alternative interactive proof system model using oracles as provers and every language accepted by these models lies in nondeterministic exponential time. Expand
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References

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We show a rough equivalence between alternating time-space complexity and a public-coin interactive proof system with the verifier having a polynomial related time-space complexity. Special casesExpand
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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
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
On the Power of Multi-Prover Interactive Protocols
TLDR
This model, developed by Ben-Or et al. (1988) allows the verifier to play the provers off each other, is shown equivalent to an alternative interactive proof system model using oracles as provers and every language accepted by these models lies in nondeterministic exponential time. Expand
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In this paper, it is proven that when both randomization and interaction are allowed, the proofs that can be verified in polynomial time are exactly those proofs that can be generated with polynomialExpand
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Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage. rhe ACM copyright notice and the title ofExpand
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
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