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RANDOM
1997
Springer
13 years 9 months ago
A Combinatorial Consistency Lemma with Application to Proving the PCP Theorem
The current proof of the 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 r...
Oded Goldreich, Shmuel Safra
STOC
2006
ACM
138views Algorithms» more  STOC 2006»
14 years 5 months ago
The PCP theorem by gap amplification
The PCP theorem [3, 2] 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 cele...
Irit Dinur
COCO
2010
Springer
186views Algorithms» more  COCO 2010»
13 years 8 months ago
Derandomized Parallel Repetition of Structured PCPs
A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return ...
Irit Dinur, Or Meir
JCT
1998
193views more  JCT 1998»
13 years 4 months ago
Fractional Kernels in Digraphs
The aim of this note is to point out some combinatorial applications of a lemma of Scarf, proved first in the context of game theory. The usefulness of the lemma in combinatorics...
Ron Aharoni, Ron Holzman
CC
2008
Springer
133views System Software» more  CC 2008»
13 years 5 months ago
Hardness Amplification via Space-Efficient Direct Products
We prove a version of the derandomized Direct Product lemma for deterministic space-bounded algorithms. Suppose a Boolean function g : {0, 1}n {0, 1} cannot be computed on more th...
Venkatesan Guruswami, Valentine Kabanets