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The power of interaction

Author: Carsten Lund
Publisher: Cambridge, Mass. : MIT Press, ©1992.
Series: ACM distinguished dissertations.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Presents an algebraic technique for constructing interactive proof systems and demonstrates the power of randomization and interaction in proving statements efficiently. Lund shows that two provers  Read more...

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Additional Physical Format: Online version:
Lund, Carsten, 1963-
Power of interaction.
Cambridge, Mass. : MIT Press, ©1992
(OCoLC)624477348
Document Type: Book
All Authors / Contributors: Carsten Lund
ISBN: 0262121700 9780262121705
OCLC Number: 26013103
Description: xii, 125 pages : illustrations ; 24 cm.
Contents: Part 1 Preliminaries: basic definitions - notation and basics, Boolean formulas, arithmetic formulas and expressions; computational models - deterministic computation, probabilistic computation, non-deterministic computation, alternating computation, interactive proof system, multiple prover interactive proof systems; computation relative to an oracle; complexity classes - deterministic complexity classes, probabilistic complexity classes, non-deterministic complexity clases, alternatiing complexity classes, interactive proof system complexity classes, non-uniform complexity classes, complexity classes relative to oracles; counting clases; completeness; summary of our results. Part 2 The power of interaction with one prover: proof systems for #P - arithmetizing of #P, proof systems for #P; proof systems for PSPaCE - arithmetizing of PSPACE, proof systems for PSPACE. Part 3 The power of interaction with two provers: another characterization of MIP; arithmetization of NEXP computation; multiple prover interactive proofs for NEXP - implementing the protocol with two provers, the power of the provers; verification of multilinear functions - the test for multilinearity, the expansion Lemma, the self-improvement Lemma, the pasting Lemma, the tree colouring Lemma. Part 4 Interaction versus alternation: restricted alternating turing machines; arithmetization of alternating computation; interactive proof systems for ATISP (t,s); alternating turing machines for pIPTISP(t,s); a hierarchy for pIPTISP(t,s); interactive proof systems for deterministic computation. Part 5 Implications and open problems: bounded-round interactive proofs; zero-knowledge; program testing and verification - robustness, instance checking, self-testing and self-correcting programs, comparison with the Blum-Luby-Rubinfield model; uniform vs. nonuniform complexity; recent developments; further research.
Series Title: ACM distinguished dissertations.
Responsibility: Carsten Lund.

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