Complexity measures on symmetric group and beyond

Neta Dafni, Yuval Filmus, Noam Lifshitz, Nathan Lindzey and Marc Vinyals
ITCS 2021

We extend the theory of complexity measures of functions beyond the Boolean cube, to domains such as the symmetric group. We show that complexity measures such as degree, approximate degree, decision tree complexity, certificate complexity, block sensitivity and sensitivity are all polynomially related for many of these domains.

In addition, we characterize Boolean degree 1 functions on the perfect matching scheme, and simplify the proof of uniqueness for $t$-intersecting families of permutations and perfect matchings.


author = {Neta Dafni and Yuval Filmus and Noam Lifshitz and Nathan Lindzey and Marc Vinyals},
title = {Complexity measures on symmetric group and beyond},
booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
year = {2021}}
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