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 language | English |
|---|---|
| Pages (from-to) | 3938-3946 |
| Number of pages | 9 |
| Journal | Theoretical Computer Science |
| Volume | 411 |
| Issue number | 44-46 |
| DOIs | |
| Publication status | Published - Oct 25 2010 |
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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 journal › Article
}
TY - JOUR
T1 - Energy and depth of threshold circuits
AU - Uchizawa, Kei
AU - Nishizeki, Takao
AU - Takimoto, Eiji
PY - 2010/10/25
Y1 - 2010/10/25
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77957669961&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77957669961&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2010.08.006
DO - 10.1016/j.tcs.2010.08.006
M3 - Article
AN - SCOPUS:77957669961
VL - 411
SP - 3938
EP - 3946
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
IS - 44-46
ER -