Computational Power of Threshold Circuits of Energy at most Two

Hiroki MANIWA  Takayuki OKI  Akira SUZUKI  Kei UCHIZAWA  Xiao ZHOU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.9   pp.1431-1439
Publication Date: 2018/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1431
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
circuit complexity,  energy complexity,  MOD function,  neural network,  threshold circuit,  

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Summary: 
The energy of a threshold circuit C is defined to be the maximum number of gates outputting ones for an input assignment, where the maximum is taken over all the input assignments. In this paper, we study computational power of threshold circuits of energy at most two. We present several results showing that the computational power of threshold circuits of energy one and the counterpart of energy two are remarkably different. In particular, we give an explicit function which requires an exponential size for threshold circuits of energy one, but is computable by a threshold circuit of size just two and energy two. We also consider MOD functions and Generalized Inner Product functions, and show that these functions also require exponential size for threshold circuits of energy one, but are computable by threshold circuits of substantially less size and energy two.