TY - GEN

T1 - Energy complexity and depth of threshold circuits

AU - Uchizawa, Kei

AU - Nishizeki, Takao

AU - Takimoto, Eiji

PY - 2009/11/9

Y1 - 2009/11/9

N2 - 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.

AB - 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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U2 - 10.1007/978-3-642-03409-1_30

DO - 10.1007/978-3-642-03409-1_30

M3 - Conference contribution

AN - SCOPUS:70350633952

SN - 364203408X

SN - 9783642034084

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 335

EP - 345

BT - Fundamentals of Computation Theory - 17th International Symposium, FCT 2009, Proceedings

T2 - 17th International Symposium on Fundamentals of Computation Theory, FCT 2009

Y2 - 2 September 2009 through 4 September 2009

ER -