Energy and fan-in of logic circuits computing symmetric Boolean functions

Akira Suzuki, Kei Uchizawa, Xiao Zhou

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we consider a logic circuit (i.e., a combinatorial circuit consisting of gates, each of which computes a Boolean function) C computing a symmetric Boolean function f, and investigate a relationship between two complexity measures, energy e and fan-in l of C, where the energy e is the maximum number of gates outputting "1" over all inputs to C, and the fan-in l is the maximum number of inputs of every gate in C. We first prove that any symmetric Boolean function f of n variables can be computed by a logic circuit of energy e=O(n/l) and fan-in l, and then provide an almost tight lower bound e≥âŒ̂(n-mf)/l⌉ where mf is the maximum numbers of consecutive "0"s or "1"s in the value vector of f. Our results imply that there exists a tradeoff between the energy and fan-in of logic circuits computing a symmetric Boolean function.

Original languageEnglish
Pages (from-to)74-80
Number of pages7
JournalTheoretical Computer Science
Publication statusPublished - 2013


  • Boolean functions
  • Energy complexity
  • Fan-in
  • MOD functions
  • Parity function
  • Symmetric functions
  • Threshold circuits


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