The Parity Problem in the Presence of Noise, Decoding Random Linear Codes, and the Subset Sum Problem

@inproceedings{Lyubashevsky2005ThePP,
  title={The Parity Problem in the Presence of Noise, Decoding Random Linear Codes, and the Subset Sum Problem},
  author={Vadim Lyubashevsky},
  booktitle={APPROX-RANDOM},
  year={2005}
}
In (2), Blum et al. demonstrated the first sub-exponential algorithm for learning the parity function in the presence of noise. They solved the length-n parity problem in time 2 O(n/ log n) but it required the availability of 2 O(n/ log n) labeled examples. As an open problem, they asked whether there exists a 2 o(n) algorithm for the length-n parity problem that uses only poly(n) labeled examples. In this work, we provide a positive answer to this question. We show that there is an algorithm… CONTINUE READING

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