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Revision #1 to TR96-047 | 20th October 1996 00:00

A Combinatorial Consistency Lemma with application to the PCP Theorem Revision of: TR96-047

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Abstract:


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 refer to the difficulty of obtaining strong results
regarding low-degree tests; namely, results of the type obtained and
used by Arora and Safra and Arora~et.~al.

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 get rid of low-degree tests altogether,
using our results it is now possible to prove the PCP Theorem
using a simple analysis of low-degree tests (which yields weaker bounds).
In other words, we replace the complicated algebraic analysis
of low-degree tests presented by Arora and Safra and Arora~et.~al.
by an intuitive combinatorial lemma
(which does not refer to low-degree tests or polynomials).


Paper:

TR96-047 | 2nd September 1996 00:00

A Combinatorial Consistency Lemma with application to the PCP Theorem


Abstract:


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 refer to the difficulty of obtaining strong results
regarding low-degree tests; namely, results of the type obtained and
used by Arora and Safra and Arora~et.~al.

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 get rid of low-degree tests altogether,
using our results it is now possible to prove the PCP Theorem
using a simple analysis of low-degree tests (which yields weaker bounds).
In other words, we replace the complicated algebraic analysis
of low-degree tests presented by Arora and Safra and Arora~et.~al.
by an intuitive combinatorial lemma
(which does not refer to low-degree tests or polynomials).



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