TY - GEN
T1 - Boolean function analysis on high-dimensional expanders
AU - Dikstein, Yotam
AU - Dinur, Irit
AU - Filmus, Yuval
AU - Harsha, Prahladh
N1 - Publisher Copyright:
© 2018 Aditya Bhaskara and Srivatsan Kumar.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - We initiate the study of Boolean function analysis on high-dimensional expanders. We describe an analog of the Fourier expansion and of the Fourier levels on simplicial complexes, and generalize the FKN theorem to high-dimensional expanders. Our results demonstrate that a high-dimensional expanding complex X can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing |X(k)| = O(n) points in comparison to . n k+1 points in the (k + 1)-slice (which consists of all n-bit strings with exactly k + 1 ones).
AB - We initiate the study of Boolean function analysis on high-dimensional expanders. We describe an analog of the Fourier expansion and of the Fourier levels on simplicial complexes, and generalize the FKN theorem to high-dimensional expanders. Our results demonstrate that a high-dimensional expanding complex X can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing |X(k)| = O(n) points in comparison to . n k+1 points in the (k + 1)-slice (which consists of all n-bit strings with exactly k + 1 ones).
KW - Boolean Function Analysis
KW - High Dimensional Expanders
KW - Sparse Model
UR - http://www.scopus.com/inward/record.url?scp=85052469709&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.APPROX-RANDOM.2018.38
DO - 10.4230/LIPIcs.APPROX-RANDOM.2018.38
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AN - SCOPUS:85052469709
SN - 9783959770859
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018
A2 - Blais, Eric
A2 - Rolim, Jose D. P.
A2 - Steurer, David
A2 - Jansen, Klaus
T2 - 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018
Y2 - 20 August 2018 through 22 August 2018
ER -