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Probabilistically Checkable Proofs, Agreement Tests, and High Dimensional Expanders

Objective

PCPs capture a striking local to global phenomenon in which a global object such as an NP witness can be checked using local constraints, and its correctness is guaranteed even if only a fraction of the constraints are satisfied.

PCPs are tightly related to hardness of approximation. The relation is essentially due to the fact that exact optimization problems can be reduced to their approximation counterparts through this local to global connection.

We view this local to global connection is a type of high dimensional expansion, akin to relatively new notions of high dimensional expansion (such as coboundary and cosystolic expansion) that have been introduced in the literature recently. We propose to study PCPs and high dimensional expansion together. We describe a concrete notion of “agreement expansion” and propose a systematic study of this question. We show how progress on agreement expansion questions is directly related to some of the most important open questions in PCPs such as the unique games conjecture, and the problem of constructing linear size PCPs.

We also propose to study the phenomenon of high dimensional expansion more broadly and to investigate its relation and applicability to questions in computational complexity that go beyond PCPs, in particular for hardness amplification and for derandomizing direct product constructions.

Keywords

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Programme(s)

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Topic(s)

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Funding Scheme

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ERC-COG - Consolidator Grant

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Call for proposal

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(opens in new window) ERC-2017-COG

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Host institution

WEIZMANN INSTITUTE OF SCIENCE
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 1 512 035,00
Address
HERZL STREET 234
7610001 Rehovot
Israel

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Activity type
Higher or Secondary Education Establishments
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Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 1 512 035,00

Beneficiaries (1)

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