Energy-efficient threshold circuits computing MOD functions

Akira Suzuki, Kei Uchizawa, Xiao Zhou

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We prove that the modulus function MODm of n variables can be computed by a threshold circuit C of energy e and size s = O(e(n/m) 1/(e - 1)) for any integer e ≥ 2, where the energy e is defined to be the maximum number of gates outputting "1" over all inputs to C, and the size s to be the number of gates in C. Our upper bound on the size s almost matches the known lower bound s = Ω(e(n/m)1/e). We also consider an extreme case where threshold circuits have energy 1, and prove that such circuits need at least 2(n - m)/2 gates to compute MOD m of n variables.

Original languageEnglish
Pages (from-to)15-29
Number of pages15
JournalInternational Journal of Foundations of Computer Science
Issue number1
Publication statusPublished - 2013 Jan


  • Circuit complexity
  • Energy complexity
  • Neural networks
  • Threshold circuits


Dive into the research topics of 'Energy-efficient threshold circuits computing MOD functions'. Together they form a unique fingerprint.

Cite this