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arXiv · 2209.03573

Quasi-Random Influences of Boolean Functions

Fan Chung·Nicholas Sieger
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Abstract

We examine a hierarchy of equivalence classes of quasi-random properties of Boolean Functions. In particular, we prove an equivalence between a number of properties including balanced influences, spectral discrepancy, local strong regularity, homomorphism enumerations of colored or weighted graphs and hypergraphs associated with Boolean functions as well as the $k$th-order strict avalanche criterion amongst others. We further construct families of quasi-random boolean functions which exhibit the properties of our equivalence theorem and separate the levels of our hierarchy.

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Fan Chung, Nicholas Sieger. 2022-09-08. Quasi-Random Influences of Boolean Functions. https://arxiv.org/abs/2209.03573

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