STRONGPCP

Strong Probabilistically Checkable Proofs

Coordinatore	WEIZMANN INSTITUTE OF SCIENCE    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Israel [IL]
Totale costo	1˙639˙584 €
EC contributo	1˙639˙584 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2009-StG
Funding Scheme	ERC-SG
Anno di inizio	2009
Periodo (anno-mese-giorno)	2009-09-01   -   2016-06-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	WEIZMANN INSTITUTE OF SCIENCE  Organization address address: HERZL STREET 234 city: REHOVOT postcode: 7610001 contact info Titolo: Ms. Nome: Gabi Cognome: Bernstein Email: send email Telefono: +972 8 934 6728 Fax: +972 8 934 4165	IL (REHOVOT)	hostInstitution	1˙639˙584.00
2	WEIZMANN INSTITUTE OF SCIENCE  Organization address address: HERZL STREET 234 city: REHOVOT postcode: 7610001 contact info Titolo: Prof. Nome: Irit Cognome: Dveer Dinur Email: send email Telefono: +972 8 9342828 Fax: +972 8 934 4122	IL (REHOVOT)	hostInstitution	1˙639˙584.00

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 Obiettivo del progetto (Objective)

'Probabilistically Checkable Proofs (PCPs) encapsulate the striking idea that verification of proofs becomes nearly trivial if one is willing to use randomness. The PCP theorem, proven in the early 90's, is a cornerstone of modern computational complexity theory. It completely revises our notion of a proof, leading to an amazingly robust behavior: A PCP proof is guaranteed to have an abundance of errors if attempting to prove a falsity. This stands in sharp contrast to our classical notion of a proof whose correctness can collapse due to one wrong step. An important drive in the development of PCP theory is the revolutionary effect it had on the field of approximation. Feige et. al. [JACM, 1996] discovered that the PCP theorem is *equivalent* to the inapproximability of several classical optimization problems. Thus, PCP theory has resulted in a leap in our understanding of approximability and opened the gate to a flood of results. To date, virtually all inapproximability results are based on the PCP theorem, and while there is an impressive body of work on hardness-of-approximation, much work still lies ahead. The central goal of this proposal is to obtain stronger PCPs than currently known, leading towards optimal inapproximability results and novel notions of robustness in computation and in proofs. This study will build upon (i) new directions opened up by my novel proof of the PCP theorem [JACM, 2007]; and on (ii) state-of-the-art PCP machinery involving techniques from algebra, functional and harmonic analysis, probability, combinatorics, and coding theory. The broader impact of this study spans a better understanding of limits for approximation algorithms saving time and resources for algorithm designers; and new understanding of robustness in a variety of mathematical contexts, arising from the many connections between PCPs and stability questions in combinatorics, functional analysis, metric embeddings, probability, and more.'