Complexity Measures on the Symmetric Group and Beyond (Extended Abstract).

Neta Dafni, Yuval Filmus, Noam Lifshitz, Nathan Lindzey, Marc Vinyals

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We extend the definitions of complexity measures of functions to domains such as the symmetric group. The complexity measures we consider include degree, approximate degree, decision tree complexity, sensitivity, block sensitivity, and a few others. We show that these complexity measures are polynomially related for the symmetric group and for many other domains. To show that all measures but sensitivity are polynomially related, we generalize classical arguments of Nisan and others. To add sensitivity to the mix, we reduce to Huang’s sensitivity theorem using “pseudo-characters”, which witness the degree of a function. Using similar ideas, we extend the characterization of Boolean degree 1 functions on the symmetric group due to Ellis, Friedgut and Pilpel to the perfect matching scheme. As another application of our ideas, we simplify the characterization of maximum-size t-intersecting families in the symmetric group and the perfect matching scheme.

Original languageAmerican English
Title of host publication12th Innovations in Theoretical Computer Science Conference, ITCS 2021
EditorsJames R. Lee
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages87:1-87:5
Number of pages5
ISBN (Electronic)9783959771771
DOIs
StatePublished - 1 Feb 2021
Event12th Innovations in Theoretical Computer Science Conference, ITCS 2021 - Virtual, Online
Duration: 6 Jan 20218 Jan 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume185

Conference

Conference12th Innovations in Theoretical Computer Science Conference, ITCS 2021
CityVirtual, Online
Period6/01/218/01/21

Keywords

  • Analysis of boolean functions
  • Complexity measures
  • Computational complexity theory
  • Extremal combinatorics

All Science Journal Classification (ASJC) codes

  • Software

Fingerprint

Dive into the research topics of 'Complexity Measures on the Symmetric Group and Beyond (Extended Abstract).'. Together they form a unique fingerprint.

Cite this