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.
@article{10_37236_11568,
author = {Nicholas Sieger and Fan Chung},
title = {Quasi-random {Boolean} functions},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {2},
doi = {10.37236/11568},
zbl = {1543.94821},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11568/}
}
TY - JOUR
AU - Nicholas Sieger
AU - Fan Chung
TI - Quasi-random Boolean functions
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11568/
DO - 10.37236/11568
ID - 10_37236_11568
ER -
%0 Journal Article
%A Nicholas Sieger
%A Fan Chung
%T Quasi-random Boolean functions
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11568/
%R 10.37236/11568
%F 10_37236_11568
Nicholas Sieger; Fan Chung. Quasi-random Boolean functions. The electronic journal of combinatorics, Tome 31 (2024) no. 2. doi: 10.37236/11568
