Energy complexity and depth of threshold circuits

Kei Uchizawa, Takao Nishizeki, Eiji Takimoto

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

2 Citations (Scopus)

Abstract

In the paper we show that there is a close relationship between the energy complexity and the depth of threshold circuits computing any Boolean function although they have completely different physical meanings. Suppose that a Boolean function f can be computed by a threshold circuit C of energy complexity e and hence at most e threshold gates in C output "1" for any input to C. We then prove that the function f can be computed also by a threshold circuit C′ of depth 2e + 1 and hence the parallel computation time of C′ is 2e + 1. If the size of C is s, that is, there are s threshold gates in C, then the size s′ of C′ is s′ = 2es + 1. Thus, if the size s of C is polynomial in the number n of input variables, then the size s′ of C′ is polynomial in n, too.

Original languageEnglish
Title of host publicationFundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings
Pages335-345
Number of pages11
DOIs
Publication statusPublished - Nov 9 2009
Event17th International Symposium on Fundamentals of Computation Theory, FCT 2009 - Wroclaw, Poland
Duration: Sep 2 2009Sep 4 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5699 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th International Symposium on Fundamentals of Computation Theory, FCT 2009
CountryPoland
CityWroclaw
Period9/2/099/4/09

Fingerprint

Threshold Circuits
Boolean functions
Networks (circuits)
Boolean Functions
Energy
Polynomials
Polynomial
Parallel Computation
Computing
Output

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Uchizawa, K., Nishizeki, T., & Takimoto, E. (2009). Energy complexity and depth of threshold circuits. In Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings (pp. 335-345). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5699 LNCS). https://doi.org/10.1007/978-3-642-03409-1_30

Energy complexity and depth of threshold circuits. / Uchizawa, Kei; Nishizeki, Takao; Takimoto, Eiji.

Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings. 2009. p. 335-345 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5699 LNCS).

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

Uchizawa, K, Nishizeki, T & Takimoto, E 2009, Energy complexity and depth of threshold circuits. in Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5699 LNCS, pp. 335-345, 17th International Symposium on Fundamentals of Computation Theory, FCT 2009, Wroclaw, Poland, 9/2/09. https://doi.org/10.1007/978-3-642-03409-1_30
Uchizawa K, Nishizeki T, Takimoto E. Energy complexity and depth of threshold circuits. In Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings. 2009. p. 335-345. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-03409-1_30
Uchizawa, Kei ; Nishizeki, Takao ; Takimoto, Eiji. / Energy complexity and depth of threshold circuits. Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings. 2009. pp. 335-345 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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