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. Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2017-COG - ERC Consolidator Grant Call for proposal ERC-2017-COG See other projects for this call Funding Scheme ERC-COG - Consolidator Grant Host institution WEIZMANN INSTITUTE OF SCIENCE Net EU contribution € 1 512 035,00 Address HERZL STREET 234 7610001 Rehovot Israel See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 512 035,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all WEIZMANN INSTITUTE OF SCIENCE Israel Net EU contribution € 1 512 035,00 Address HERZL STREET 234 7610001 Rehovot See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 512 035,00
