Energy and depth of threshold circuits

Kei Uchizawa, Takao Nishizeki, Eiji Takimoto

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this 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 prove that the function f can also be computed by a threshold circuit C′ of the 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
Pages (from-to)3938-3946
Number of pages9
JournalTheoretical Computer Science
Volume411
Issue number44-46
DOIs
Publication statusPublished - Oct 25 2010

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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

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

In: Theoretical Computer Science, Vol. 411, No. 44-46, 25.10.2010, p. 3938-3946.

Research output: Contribution to journalArticle

Uchizawa, Kei ; Nishizeki, Takao ; Takimoto, Eiji. / Energy and depth of threshold circuits. In: Theoretical Computer Science. 2010 ; Vol. 411, No. 44-46. pp. 3938-3946.
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