Energy-efficient threshold circuits detecting global pattern in 1-dimentional arrays

Akira Suzuki, Kei Uchizawa, Gyo Shu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

In this paper, we investigate a relationship between energy and size of a threshold circuit processing a simple task, called PLR n, that was introduced in a context of pattern recognition. Formally, P LR n: {0, 1}n x {0, 1}n → {0,1} is defined as follows: For every x = (x1,x2,⋯, xn) ∈ {0, 1}n and y = (y1,y 2,⋯,yn) ∈ {0, 1}n, PLR n(x, y) = 1 if there exists a pair of indices i and j such that i < j and xi = yj = 1; and PLR n(x,y) = 0 otherwise. We prove that PLR n can be computed by a threshold circuit of energy e and size s = O (e · n 2/e-1) for any integer e, 3 ≤ e ≤ 2log2 n + 1. Our result implies that one can construct an energy-efficient circuit computing PLR n if it is allowable to use large size. Moreover, we focus on an extreme case where a threshold circuit has energy e = 1, and show that PLR can be computed by a threshold circuit of energy e = 1 and size s = ⌊n/2⌋, while PLR n cannot be computed by any threshold circuit of energy e = 1 and size s ≤ ⌊n/2⌋ - 1.

Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation - 10th International Conference, TAMC 2013, Proceedings
PublisherSpringer-Verlag
Pages248-259
Number of pages12
ISBN (Print)9783642382352
DOIs
Publication statusPublished - 2013 Jan 1
Event10th International Conference on Theory and Applications of Models of Computation, TAMC 2013 - Hong Kong, China
Duration: 2013 May 202013 May 22

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7876 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Conference on Theory and Applications of Models of Computation, TAMC 2013
CountryChina
CityHong Kong
Period13/5/2013/5/22

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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    Suzuki, A., Uchizawa, K., & Shu, G. (2013). Energy-efficient threshold circuits detecting global pattern in 1-dimentional arrays. In Theory and Applications of Models of Computation - 10th International Conference, TAMC 2013, Proceedings (pp. 248-259). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7876 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-642-38236-9_23