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TR24-009 | 20th January 2024 18:46
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#### Unambiguous parity-query complexity

**Abstract:**
We give a lower bound of ?(?n) on the unambiguous randomised parity-query complexity of the approximate majority problem – that is, on the lowest randomised parity-query complexity of any function over {0,1}? whose value is "0" if the Hamming weight of the input is at most n/3, is "1" if the weight is at least 2n/3, and may be arbitrary otherwise.

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Comment #1 to TR24-009 | 21st January 2024 14:59
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#### Unambiguous parity-query complexity

**Comment:**
We give a lower bound of $\Omega(\sqrt n)$ on the unambiguous randomised parity-query complexity of the approximate majority problem – that is, on the lowest randomised parity-query complexity of any function over ${0,1}^n$ whose value is "0"; if the Hamming weight of the input is at most n/3, is "1"; if the weight is at least 2n/3, and may be arbitrary otherwise.