The book by Arora and Barak contains in chapter notes on PCPWe note that Dinur's general strategy is somewhat reminiscent of the zig-zag construction of expander graphs and Reingold's deterministic logspace algorithm for undirected connectivity described in Chapter 20, which suggests that more connections are waiting to be made between these different areas of research. (pg 494)What precisely is meant by this reminiscence? Is there a common property/lemma than can be factored out of these two proofs?
Connection between PCP and L=SL
cc.complexity theory;pcp
The precise answer to your question is given by Oded Goldreich in his article Bravely, Moderately: A Common Theme in Four Recent Works.Here is the link: http://www.wisdom.weizmann.ac.il/~oded/COL/brave.pdf