Assignment Testers: Towards a Combinatorial Proof of the PCP-Theorem

In this work we look back into the proof of the PCP Theorem, with the goal of finding new proofs that are "more combinatorial" and arguably simpler. For that we introduce the notion of an assignment tester, which is a strengthening of the standard PCP verifier, in the following sense. Given a statement and an alleged proof for it, while the PCP verifier checks correctness of the statement, the assignment-tester checks correctness of the statement and the proof. This notion enables composition that is truly modular, i.e., one can compose two assignment-testers without any assumptions on how they are constructed. A related notion called PCPs of Proximity was independently introduced in [BSGH+ 04]. We provide a toolkit of (non-trivial) generic transformations on assignment testers. These transformations may be interesting in their own right, and allow us to present the following two main results:

• Type: Conference
• Year: 2004
• Where: FOCS
• Authors: Irit Dinur, Omer Reingold
• Keywords: Assignment Testers, FOCS 2004, PCP Verifier, Standard Pcp Verifier, Theoretical Computer Science