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

Kei Uchizawa; Eiji Takimoto

doi:10.1109/CCC.2007.4

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 proceeding › Conference 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 language	English
Title of host publication	Proceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007
Pages	169-178
Number of pages	10
DOIs	https://doi.org/10.1109/CCC.2007.4
Publication status	Published - Oct 2 2007
Externally published	Yes
Event	22nd Annual IEEE Conference on Computational Complexity, CCC 2007 - San Diego, CA, United States Duration: Jun 13 2007 → Jun 16 2007

Publication series

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

Other

Other	22nd Annual IEEE Conference on Computational Complexity, CCC 2007
Country	United States
City	San Diego, CA
Period	6/13/07 → 6/16/07

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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 proceeding › Conference 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

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Access to Document

10.1109/CCC.2007.4