A Structural Theorem for Local Algorithms with Applications to Coding, Testing, and Privacy

  title={A Structural Theorem for Local Algorithms with Applications to Coding, Testing, and Privacy},
  author={Marcel Dall'Agnol and Tom Gur and Oded Lachish},
  booktitle={Electron. Colloquium Comput. Complex.},
We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes $q$ adaptive queries and satisfies a natural robustness condition admits a sample-based algorithm with $n^{1- 1/O(q^2 \log^2 q)}$ sample complexity, following the definition of Goldreich and Ron (TOCT 2016). We prove that this transformation is nearly optimal. Our theorem also admits… 
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