On Dinur’s Proof of the PCP Theorem

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Afshari, Behnam | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42616 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Daneshgar, Amir
Abstract:
The PCP theorem is the result of a line of work on interactive proofs and probabilistically checkable proofs. The first theorem relating standard proofs and probabilistically checkable proofs is NEXP?PCP[poly(n),poly(n)] . Subsequently, the method used in the proof of this statement were extended to yield a proof of the PCP theorem. However, this proof is relatively long and complicated. The PCP theorem is equivalent to hardness of approximation of some optimization problems. In 2006, Irit Dinur discovered a different proof of the PCP theorem. Dinur’s proof is a rather shorter and simpler than original proof. The main purpose of this survey is to present the main concepts and tools used in Dinur's proof of the PCP theorem
Keywords:
Expander Graph ; Error Correction Codes ; Probabilistic Checkable Proof ; Local Testability ; Random Walk