Matches in SemOpenAlex for { <https://semopenalex.org/work/W336776360> ?p ?o ?g. }
Showing items 1 to 97 of
97
with 100 items per page.
- W336776360 abstract "The PCP theorem [Arora and Safra 1998; Arora et. al. 1998] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The celebrated equivalence of this theorem and inapproximability of certain optimization problems, due to Feige et al. [1996], has placed the PCP theorem at the heart of the area of inapproximability.In this work, we present a new proof of the PCP theorem that draws on this equivalence. We give a combinatorial proof for the NP-hardness of approximating a certain constraint satisfaction problem, which can then be reinterpreted to yield the PCP theorem.Our approach is to consider the unsat value of a constraint system, which is the smallest fraction of unsatisfied constraints, ranging over all possible assignments for the underlying variables. We describe a new combinatorial amplification transformation that doubles the unsat-value of a constraint-system, with only a linear blowup in the size of the system. The amplification step causes an increase in alphabet-size that is corrected by a (standard) PCP composition step. Iterative application of these two steps yields a proof for the PCP theorem.The amplification lemma relies on a new notion of “graph powering” that can be applied to systems of binary constraints. This powering amplifies the unsat-value of a constraint system provided that the underlying graph structure is an expander.We also extend our amplification lemma towards construction of assignment testers (alternatively, PCPs of Proximity) which are slightly stronger objects than PCPs. We then construct PCPs and locally-testable codes whose length is linear up to a polylog factor, and whose correctness can be probabilistically verified by making a constant number of queries. Namely, we prove SAT ∈ PCP1/2,1[log2(n⋅poly log n), O(1)]." @default.
- W336776360 created "2016-06-24" @default.
- W336776360 creator A5029616850 @default.
- W336776360 date "2005-01-01" @default.
- W336776360 modified "2023-09-26" @default.
- W336776360 title "The PCP theorem by gap amplification" @default.
- W336776360 cites W1483094817 @default.
- W336776360 cites W1542241645 @default.
- W336776360 cites W1595252626 @default.
- W336776360 cites W1970259241 @default.
- W336776360 cites W1970606468 @default.
- W336776360 cites W1978478346 @default.
- W336776360 cites W1999032440 @default.
- W336776360 cites W2017899870 @default.
- W336776360 cites W2018047324 @default.
- W336776360 cites W2019578639 @default.
- W336776360 cites W2022381972 @default.
- W336776360 cites W2029859729 @default.
- W336776360 cites W2038225707 @default.
- W336776360 cites W2073310493 @default.
- W336776360 cites W2080578129 @default.
- W336776360 cites W2082647621 @default.
- W336776360 cites W2096390054 @default.
- W336776360 cites W2097206148 @default.
- W336776360 cites W2106110343 @default.
- W336776360 cites W2111385661 @default.
- W336776360 cites W2141815340 @default.
- W336776360 cites W2146261818 @default.
- W336776360 cites W2149815049 @default.
- W336776360 cites W2166162093 @default.
- W336776360 cites W2293231900 @default.
- W336776360 cites W2404719651 @default.
- W336776360 hasPublicationYear "2005" @default.
- W336776360 type Work @default.
- W336776360 sameAs 336776360 @default.
- W336776360 citedByCount "2" @default.
- W336776360 crossrefType "journal-article" @default.
- W336776360 hasAuthorship W336776360A5029616850 @default.
- W336776360 hasConcept C105795698 @default.
- W336776360 hasConcept C114614502 @default.
- W336776360 hasConcept C118615104 @default.
- W336776360 hasConcept C132525143 @default.
- W336776360 hasConcept C18903297 @default.
- W336776360 hasConcept C199622910 @default.
- W336776360 hasConcept C2524010 @default.
- W336776360 hasConcept C2776036281 @default.
- W336776360 hasConcept C2777759810 @default.
- W336776360 hasConcept C2780069185 @default.
- W336776360 hasConcept C33923547 @default.
- W336776360 hasConcept C46757340 @default.
- W336776360 hasConcept C48372109 @default.
- W336776360 hasConcept C49937458 @default.
- W336776360 hasConcept C86803240 @default.
- W336776360 hasConcept C94375191 @default.
- W336776360 hasConceptScore W336776360C105795698 @default.
- W336776360 hasConceptScore W336776360C114614502 @default.
- W336776360 hasConceptScore W336776360C118615104 @default.
- W336776360 hasConceptScore W336776360C132525143 @default.
- W336776360 hasConceptScore W336776360C18903297 @default.
- W336776360 hasConceptScore W336776360C199622910 @default.
- W336776360 hasConceptScore W336776360C2524010 @default.
- W336776360 hasConceptScore W336776360C2776036281 @default.
- W336776360 hasConceptScore W336776360C2777759810 @default.
- W336776360 hasConceptScore W336776360C2780069185 @default.
- W336776360 hasConceptScore W336776360C33923547 @default.
- W336776360 hasConceptScore W336776360C46757340 @default.
- W336776360 hasConceptScore W336776360C48372109 @default.
- W336776360 hasConceptScore W336776360C49937458 @default.
- W336776360 hasConceptScore W336776360C86803240 @default.
- W336776360 hasConceptScore W336776360C94375191 @default.
- W336776360 hasLocation W3367763601 @default.
- W336776360 hasOpenAccess W336776360 @default.
- W336776360 hasPrimaryLocation W3367763601 @default.
- W336776360 hasRelatedWork W1605144615 @default.
- W336776360 hasRelatedWork W184142732 @default.
- W336776360 hasRelatedWork W1978478346 @default.
- W336776360 hasRelatedWork W2010886177 @default.
- W336776360 hasRelatedWork W2019578639 @default.
- W336776360 hasRelatedWork W2078090052 @default.
- W336776360 hasRelatedWork W2084204509 @default.
- W336776360 hasRelatedWork W2091602684 @default.
- W336776360 hasRelatedWork W2143112402 @default.
- W336776360 hasRelatedWork W2148352980 @default.
- W336776360 hasRelatedWork W2153413398 @default.
- W336776360 hasRelatedWork W2394548550 @default.
- W336776360 hasRelatedWork W2395412869 @default.
- W336776360 hasRelatedWork W239882307 @default.
- W336776360 hasRelatedWork W2403422998 @default.
- W336776360 hasRelatedWork W2405388088 @default.
- W336776360 hasRelatedWork W2950088100 @default.
- W336776360 hasRelatedWork W3119413233 @default.
- W336776360 hasRelatedWork W3179120893 @default.
- W336776360 hasRelatedWork W2146392217 @default.
- W336776360 isParatext "false" @default.
- W336776360 isRetracted "false" @default.
- W336776360 magId "336776360" @default.
- W336776360 workType "article" @default.