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On the Probabilistic Degrees of Symmetric Boolean Functions

Authors Srikanth Srinivasan, Utkarsh Tripathi, S. Venkitesh

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Author Details

Srikanth Srinivasan
  • Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India
Utkarsh Tripathi
  • Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India
S. Venkitesh
  • Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India

Funding

  • Srinivasan, Srikanth: Supported by MATRICS grant MTR/2017/000958 awarded by SERB, Government of India.
  • Tripathi, Utkarsh: Supported by the Ph.D. Scholarship of NBHM, DAE, Government of India.
  • Venkitesh, S.: Supported by the Senior Research Fellowship of HRDG, CSIR, Government of India.

Cite As Get BibTex

Srikanth Srinivasan, Utkarsh Tripathi, and S. Venkitesh. On the Probabilistic Degrees of Symmetric Boolean Functions. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 28:1-28:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.FSTTCS.2019.28

Abstract

The probabilistic degree of a Boolean function f:{0,1}^n -> {0,1} is defined to be the smallest d such that there is a random polynomial P of degree at most d that agrees with f at each point with high probability. Introduced by Razborov (1987), upper and lower bounds on probabilistic degrees of Boolean functions - specifically symmetric Boolean functions - have been used to prove explicit lower bounds, design pseudorandom generators, and devise algorithms for combinatorial problems. 
In this paper, we characterize the probabilistic degrees of all symmetric Boolean functions up to polylogarithmic factors over all fields of fixed characteristic (positive or zero).

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Symmetric Boolean function
  • probabilistic degree

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