An Improved Dictatorship Test with Perfect Completeness

  title={An Improved Dictatorship Test with Perfect Completeness},
  author={Amey Bhangale and Subhash Khot and Devanathan Thiruvenkatachari},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
A Boolean function f : {0, 1} → {0, 1} is called a dictator if it depends on exactly one variable i.e f(x1, x2, . . . , xn) = xi for some i ∈ [n]. In this work, we study a k-query dictatorship test. Dictatorship tests are central in proving many hardness results for constraint satisfaction problems. The dictatorship test is said to have perfect completeness if it accepts any dictator function. The soundness of a test is the maximum probability with which it accepts any function far from a… CONTINUE READING

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