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Energy Complexity and Depth of Threshold Circuits

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Fundamentals of Computation Theory (FCT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5699))

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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.

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Author information

Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Aramaki Aoba-aza 6-6-05, Aoba-ku, Sendai, 980-8579, Japan

    Kei Uchizawa & Takao Nishizeki

  2. Department of Informatics, Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Eiji Takimoto

Authors
  1. Kei Uchizawa
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  2. Takao Nishizeki
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  3. Eiji Takimoto
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Mirosław Kutyłowski  & Maciej Gębala  & 

  2. Institute of Computer Science, University of Wrocław, ul. Joliot-Curie 15, 50-383, Wrocław, Poland

    Witold Charatonik

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© 2009 Springer-Verlag Berlin Heidelberg

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Uchizawa, K., Nishizeki, T., Takimoto, E. (2009). Energy Complexity and Depth of Threshold Circuits. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds) Fundamentals of Computation Theory. FCT 2009. Lecture Notes in Computer Science, vol 5699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03409-1_30

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  • DOI: https://doi.org/10.1007/978-3-642-03409-1_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03408-4

  • Online ISBN: 978-3-642-03409-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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