An exponential lower bound on the size of constant-depth threshold circuits with small energy complexity

Kei Uchizawa, Eiji Takimoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (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 tradeoff among three complexity measures of threshold circuits: the energy complexity, size, and depth. The tradeoff 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
Title of host publicationProceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007
Pages169-178
Number of pages10
DOIs
Publication statusPublished - Oct 2 2007
Event22nd Annual IEEE Conference on Computational Complexity, CCC 2007 - San Diego, CA, United States
Duration: Jun 13 2007Jun 16 2007

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159

Other

Other22nd Annual IEEE Conference on Computational Complexity, CCC 2007
CountryUnited States
CitySan Diego, CA
Period6/13/076/16/07

Fingerprint

Threshold Circuits
Lower bound
Networks (circuits)
Energy
Boolean functions
Complexity Measure
Neurons
Boolean Functions
Brain
Neuron
Trade-offs
Spike
Imply
Output

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Computational Mathematics

Cite this

Uchizawa, K., & Takimoto, E. (2007). An exponential lower bound on the size of constant-depth threshold circuits with small energy complexity. In Proceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007 (pp. 169-178). [4262761] (Proceedings of the Annual IEEE Conference on Computational Complexity). https://doi.org/10.1109/CCC.2007.4

An exponential lower bound on the size of constant-depth threshold circuits with small energy complexity. / Uchizawa, Kei; Takimoto, Eiji.

Proceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007. 2007. p. 169-178 4262761 (Proceedings of the Annual IEEE Conference on Computational Complexity).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Uchizawa, K & Takimoto, E 2007, An exponential lower bound on the size of constant-depth threshold circuits with small energy complexity. in Proceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007., 4262761, Proceedings of the Annual IEEE Conference on Computational Complexity, pp. 169-178, 22nd Annual IEEE Conference on Computational Complexity, CCC 2007, San Diego, CA, United States, 6/13/07. https://doi.org/10.1109/CCC.2007.4
Uchizawa K, Takimoto E. An exponential lower bound on the size of constant-depth threshold circuits with small energy complexity. In Proceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007. 2007. p. 169-178. 4262761. (Proceedings of the Annual IEEE Conference on Computational Complexity). https://doi.org/10.1109/CCC.2007.4
Uchizawa, Kei ; Takimoto, Eiji. / An exponential lower bound on the size of constant-depth threshold circuits with small energy complexity. Proceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007. 2007. pp. 169-178 (Proceedings of the Annual IEEE Conference on Computational Complexity).
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