Limits of Preprocessing

Yuval Filmus, Yuval Ishai, Avi Kaplan*, Guy Kindler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

It is a classical result that the inner product function cannot be computed by an AC0 circuit. It is conjectured that this holds even if we allow arbitrary preprocessing of each of the two inputs separately. We prove this conjecture when the preprocessing of one of the inputs is limited to output n+n/(logω(1)n) bits and obtain a tight correlation bound. Our methods extend to many other functions, including pseudorandom functions, and imply a---weak yet nontrivial---limitation on the power of encoding inputs in low-complexity cryptography. Finally, under cryptographic assumptions, we relate the question of proving variants of the above conjecture with the question of learning AC0 under simple input distributions.

Original languageAmerican English
Article number5
JournalComputational Complexity
Volume33
Issue number1
DOIs
StatePublished - Jun 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Keywords

  • 68Q06
  • 68Q11
  • Circuit complexity
  • communication complexity
  • constant-depth circuit
  • IPPP
  • pseudorandom function
  • simultaneous messages

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