Matches in SemOpenAlex for { <https://semopenalex.org/work/W2294800560> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W2294800560 endingPage "102" @default.
- W2294800560 startingPage "1" @default.
- W2294800560 abstract "The Probabilistically Checkable Proof (PCP) theorem (Arora and Safra in J ACM 45(1):70–122, 1998; Arora et al. in J ACM 45(3):501–555, 1998) asserts the existence of proofs that can be verified by reading a very small part of the proof. Since the discovery of the theorem, there has been a considerable work on improving the theorem in terms of the length of the proofs, culminating in the construction of PCPs of quasi-linear length, by Ben-Sasson and Sudan (SICOMP 38(2):551–607, 2008) and Dinur (J ACM 54(3):241–250, 2007). One common theme in the aforementioned PCP constructions is that they all rely heavily on sophisticated algebraic machinery. The aforementioned work of Dinur (2007) suggested an alternative approach for constructing PCPs, which gives a simpler and arguably more intuitive proof of the PCP theorem using combinatorial techniques. However, this combinatorial construction only yields PCPs of polynomial length and is therefore inferior to the algebraic constructions in this respect. This gives rise to the natural question of whether the proof length of the algebraic constructions can be matched using the combinatorial approach. In this work, we provide a combinatorial construction of PCPs of length $${ncdotleft(log nright)^{O(loglog n)}}$$ , coming very close to the state-of-the-art algebraic constructions (whose proof length is $${ncdotleft(log nright)^{O(1)}}$$ ). To this end, we develop a few generic PCP techniques which may be of independent interest. It should be mentioned that our construction does use low-degree polynomials at one point. However, our use of polynomials is confined to the construction of error-correcting codes with a certain simple multiplication property, and it is conceivable that such codes could be constructed without the use of polynomials. In addition, we provide a variant of the main construction that does not use polynomials at all and has proof length $${n^{4} cdotleft(log nright)^{O(loglog n)}}$$ . This is already an improvement over the aforementioned combinatorial construction of Dinur." @default.
- W2294800560 created "2016-06-24" @default.
- W2294800560 creator A5071686980 @default.
- W2294800560 date "2016-01-21" @default.
- W2294800560 modified "2023-10-18" @default.
- W2294800560 title "Combinatorial PCPs with Short Proofs" @default.
- W2294800560 cites W1530008367 @default.
- W2294800560 cites W1540200135 @default.
- W2294800560 cites W1579088726 @default.
- W2294800560 cites W1970278864 @default.
- W2294800560 cites W1976493784 @default.
- W2294800560 cites W1980816908 @default.
- W2294800560 cites W2006837132 @default.
- W2294800560 cites W2019578639 @default.
- W2294800560 cites W2021413381 @default.
- W2294800560 cites W2022381972 @default.
- W2294800560 cites W2029859729 @default.
- W2294800560 cites W2036265926 @default.
- W2294800560 cites W2037858154 @default.
- W2294800560 cites W2038225707 @default.
- W2294800560 cites W2038691311 @default.
- W2294800560 cites W2045717693 @default.
- W2294800560 cites W2053086236 @default.
- W2294800560 cites W2056759312 @default.
- W2294800560 cites W2087900794 @default.
- W2294800560 cites W2132850797 @default.
- W2294800560 cites W2140797111 @default.
- W2294800560 cites W2148352980 @default.
- W2294800560 cites W2164606052 @default.
- W2294800560 cites W2293231900 @default.
- W2294800560 cites W2611428058 @default.
- W2294800560 cites W3149588634 @default.
- W2294800560 cites W4229760579 @default.
- W2294800560 doi "https://doi.org/10.1007/s00037-015-0111-x" @default.
- W2294800560 hasPublicationYear "2016" @default.
- W2294800560 type Work @default.
- W2294800560 sameAs 2294800560 @default.
- W2294800560 citedByCount "2" @default.
- W2294800560 countsByYear W22948005602016 @default.
- W2294800560 countsByYear W22948005602021 @default.
- W2294800560 crossrefType "journal-article" @default.
- W2294800560 hasAuthorship W2294800560A5071686980 @default.
- W2294800560 hasBestOaLocation W22948005602 @default.
- W2294800560 hasConcept C108710211 @default.
- W2294800560 hasConcept C114614502 @default.
- W2294800560 hasConcept C118539577 @default.
- W2294800560 hasConcept C118615104 @default.
- W2294800560 hasConcept C134306372 @default.
- W2294800560 hasConcept C161505775 @default.
- W2294800560 hasConcept C2524010 @default.
- W2294800560 hasConcept C33923547 @default.
- W2294800560 hasConcept C9376300 @default.
- W2294800560 hasConceptScore W2294800560C108710211 @default.
- W2294800560 hasConceptScore W2294800560C114614502 @default.
- W2294800560 hasConceptScore W2294800560C118539577 @default.
- W2294800560 hasConceptScore W2294800560C118615104 @default.
- W2294800560 hasConceptScore W2294800560C134306372 @default.
- W2294800560 hasConceptScore W2294800560C161505775 @default.
- W2294800560 hasConceptScore W2294800560C2524010 @default.
- W2294800560 hasConceptScore W2294800560C33923547 @default.
- W2294800560 hasConceptScore W2294800560C9376300 @default.
- W2294800560 hasIssue "1" @default.
- W2294800560 hasLocation W22948005601 @default.
- W2294800560 hasLocation W22948005602 @default.
- W2294800560 hasOpenAccess W2294800560 @default.
- W2294800560 hasPrimaryLocation W22948005601 @default.
- W2294800560 hasRelatedWork W2130523901 @default.
- W2294800560 hasRelatedWork W2164606052 @default.
- W2294800560 hasRelatedWork W2294800560 @default.
- W2294800560 hasRelatedWork W2396415655 @default.
- W2294800560 hasRelatedWork W2403422998 @default.
- W2294800560 hasRelatedWork W2999935146 @default.
- W2294800560 hasRelatedWork W3153156984 @default.
- W2294800560 hasRelatedWork W3157478331 @default.
- W2294800560 hasRelatedWork W3173957725 @default.
- W2294800560 hasRelatedWork W4297691964 @default.
- W2294800560 hasVolume "25" @default.
- W2294800560 isParatext "false" @default.
- W2294800560 isRetracted "false" @default.
- W2294800560 magId "2294800560" @default.
- W2294800560 workType "article" @default.