# Algebraic methods for interactive proof systems

@article{Lund1992AlgebraicMF, title={Algebraic methods for interactive proof systems}, author={C. Lund and L. Fortnow and H. Karloff and N. 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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#### 399 Citations

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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 cases… Expand

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We show that every language in PSPACE, or equivalently, every language accepted by an unbounded round interactive proof system, ha a 1-round, 2-prover interactive proof system with exponentially… Expand

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Several alternative formulations of the concept of an e cient proof system are nowadays coexisting in our eld These systems include the classical formulation of NP interactive proof systems giving… Expand

PSPACE is provable by two provers in one round

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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 exponentially… Expand

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It is proved that every language in PSPACE has a quantum interactive proof system that requires a total of only three messages to be sent between the prover and verifier and has exponentially small (one-sided) probability of error. Expand

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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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