TY - JOUR

T1 - Combinatorial consistency lemma with application to proving the PCP theorem

AU - Goldreich, Oded

AU - Safra, Shmuel

PY - 2000

Y1 - 2000

N2 - The current proof of the probabilistically checkable proofs (PCP) theorem (i.e., NP = PCP(log, O(1))) is very complicated. One source of difficulty is the technically involved analysis of low-degree tests. Here, we refer to the difficulty of obtaining strong results regarding low-degree tests; namely, results of the type obtained and used by Arora and Safra [J. ACM, 45 (1998), pp. 70-122] and Arora et al. [J. ACM, 45 (1998), pp. 501-555]. In this paper, we eliminate the need to obtain such strong results on low-degree tests when proving the PCP theorem. Although we do not remove the need for low-degree tests altogether, using our results it is now possible to prove the PCP theorem using a simpler analysis of low-degree tests (which yields weaker bounds). In other words, we replace the strong algebraic analysis of low-degree tests presented by Arora and Safra and Arora et al. by a combinatorial lemma (which does not refer to low-degree tests or polynomials.

AB - The current proof of the probabilistically checkable proofs (PCP) theorem (i.e., NP = PCP(log, O(1))) is very complicated. One source of difficulty is the technically involved analysis of low-degree tests. Here, we refer to the difficulty of obtaining strong results regarding low-degree tests; namely, results of the type obtained and used by Arora and Safra [J. ACM, 45 (1998), pp. 70-122] and Arora et al. [J. ACM, 45 (1998), pp. 501-555]. In this paper, we eliminate the need to obtain such strong results on low-degree tests when proving the PCP theorem. Although we do not remove the need for low-degree tests altogether, using our results it is now possible to prove the PCP theorem using a simpler analysis of low-degree tests (which yields weaker bounds). In other words, we replace the strong algebraic analysis of low-degree tests presented by Arora and Safra and Arora et al. by a combinatorial lemma (which does not refer to low-degree tests or polynomials.

UR - http://www.scopus.com/inward/record.url?scp=0033712260&partnerID=8YFLogxK

U2 - 10.1137/S0097539797315744

DO - 10.1137/S0097539797315744

M3 - מאמר

AN - SCOPUS:0033712260

VL - 29

SP - 1132

EP - 1154

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 4

ER -