New Distinguishers for Negation-Limited Weak Pseudorandom Functions
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Abstract (arXiv)
We show how to distinguish circuits with log k negations (a.k.a k-monotone functions) from uniformly random functions in expleft(tildeOleft(n1/3k2/3right)right) time using random samples. The previous best distinguisher, due to the learning algorithm by Blais, Cannone, Oliveira, Servedio, and Tan (RANDOM'15), requires expbig(tildeO(n1/2 k)big) time. Our distinguishers are based on Fourier analysis on slices of the Boolean cube. We show that some "middle" slices of negation-limited circuits have strong low-degree Fourier concentration and then we apply a variation of the classic Linial, Mansour, and Nisan "Low-Degree algorithm" (JACM'93) on slices. Our techniques also lead to a slightly improved weak learner for negation limited circuits under the uniform distribution.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 2 of its 30 references that are in the map. First posted on arXiv 23 Mar 2022.
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References · 2
- 2014Approximate resilience, monotonicity, and the complexity of agnostic learningcited by 16
- 2014Learning circuits with few negationscited by 5
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