P. Feldman. The optimum prover lives in PSPACE. Manuscript, 1986. Home/Search Document Not in Database Summary Related Articles Check |
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A Short History of Computational Complexity - Fortnow, Homer (2002) (Correct)
....not NP complete. In 1990, Lund, Fortnow, Karlo and Nisan [LFKN92] showed that the complements of NP complete languages have unbounded round interactive proof systems. Shamir [Sha92] quickly extended their techniques to show that every language in PSPACE has interactive proof system. Feldman [Fel86] had earlier shown that every language with interactive proofs lies in PSPACE. Interactive proofs are notable in that in general proofs concerning them do not relativize, that is they are not true relative to every oracle. The classi cation of interactive proofs turned out not to be the end of ....
P. Feldman. The optimum prover lives in PSPACE. Manuscript, 1986.
Interactive and Probabilistic Proof-Checking - Trevisan (2000) (Correct)
....protocol described above. Neither of these problems is known 1 One may wonder whether it is restrictive to assume that the prover is a Turing machine as opposed to an abstract device that can even solve undecidable problems; it turns out that every prover can be replaced by a prover in PSPACE [Fel86] 3 (nor believed to be) co NP hard, and for some time it was believed that IP was just slightly extending the class NP. In particular it appeared to be unlikely that interactive proofs would capture co NP. The intuitive reason is that a proof of a co NP complete statement has to provide ....
....using randomness and interaction in polynomial time. The result of [LFKN92] was even more general: they showed that the entire polynomial hierarchy is contained in IP. Shortly after, Shamir [Sha92] proved that PSPACE is contained in IP. Since the opposite containment was also known [Pap85, Fel86] the following new characterization of PSPACE had ben derived. Theorem 2 ( LFKN92, Sha92] IP=PSPACE. Unlike other results mentioned in this survey, Theorem 2 has no known application outside the theory of complexity classes. But within this area its impact has been dramatic. For starters, ....
P. Feldman. The optimum prover lives in PSPACE. Manuscript, 1986.
Algebraic Methods for Interactive Proof Systems - Lund, Fortnow, Karloff, Nisan (1992) (144 citations) (Correct)
....we develop a new technique for reducing the problem of verifying the value of a low degree polynomial at two given points to verifying the value at one new point. Shamir [S] has used this technique to prove that all languages in PSPACE have interactive proof systems. From the fact that IP PSPACE [F], it follows that IP=PSPACE. Babai, Fortnow and Lund [BFL] have also used this technique in their proof that every language in nondeterministic exponential time has a two prover interactive proof system in which the provers cannot communicate with one another. Our results also have implications ....
P. Feldman. The optimum prover lives in PSPACE. Manuscript, M.I.T., 1986.
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