Exponential lower bounds on the size of constant-depth threshold circuits with small energy complexity

Kei Uchizawa, Eiji Takimoto

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

A complexity measure for threshold circuits, called the energy complexity, has been proposed to measure an amount of energy consumed during computation in the brain. Biological neurons need more energy to transmit a "spike" than not to transmit one, and hence the energy complexity of a threshold circuit is defined as the number of gates in the circuit that output "1" during computation. Since the firing activity of neurons in the brain is quite sparse, the following question arises: what Boolean functions can or cannot be computed by threshold circuits with small energy complexity. In the paper, we partially answer the question, that is, we show that there exists a trade-off among three complexity measures of threshold circuits: the energy complexity, size, and depth. The trade-off implies an exponential lower bound on the size of constant-depth threshold circuits with small energy complexity for a large class of Boolean functions.

Original languageEnglish
Pages (from-to)474-487
Number of pages14
JournalTheoretical Computer Science
Volume407
Issue number1-3
DOIs
Publication statusPublished - Nov 6 2008

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this