Random Graphs, Spin Glasses and Percolation

Abstract

Given a function f : [n] → {0, 1}, its k-wise direct product encoding is the function F : [n]k → {0, 1}k defined by F (x1, . . . , xk) = (f(x1), . . . , f(xk)). This simple “encoding” is useful in PCP-like settings, when we want to simulate reading k arbitrary values of f by accessing only a constant number of inputs of the encoding F . The main challenge… (More)

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