On the number of ANDs versus the number of ORs in monotone Boolean circuits

Uri Zwick*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Alon and Boppana showed that if a monotone Boolean function f of n variables can be computed by a monotone circuit containing k AND gates, where k > 1, then it can also be computed using a monotone circuit containing k AND gates and O(k(n + k)) OR gates. They note that their result is tight up to a logarithmic factor. Here we show that under the same assumption the function f can be computed using a monotone circuit containing k AND gates and O(k(n + k)/ log k) OR gates. This result is tight up to a constant factor. By duality the same result holds when the roles of the AND and OR gates are interchanged.

Original languageEnglish
Pages (from-to)29-30
Number of pages2
JournalInformation Processing Letters
Volume59
Issue number1
DOIs
StatePublished - 8 Jul 1996

Keywords

  • AND and OR gates
  • Boolean complexity
  • Circuit complexity
  • Computational complexity
  • Monotone complexity

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