TY - GEN

T1 - Energy-efficient threshold circuits detecting global pattern in 1-dimentional arrays

AU - Suzuki, Akira

AU - Uchizawa, Kei

AU - Zhou, Xiao

N1 - Funding Information:
This work is partially supported by JSPS Grant-in-Aid for Scientific Research, Grant Numbers 24.3660 (A.Suzuki), 23700003 (K.Uchizawa) and 23500001 (X.Zhou).

PY - 2013

Y1 - 2013

N2 - In this paper, we investigate a relationship between energy and size of a threshold circuit processing a simple task, called PLRn, that was introduced in a context of pattern recognition. Formally, P LRn: {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 PLRn 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 PLRn 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 PLRn cannot be computed by any threshold circuit of energy e = 1 and size s ≤ ⌊n/2⌋ - 1.

AB - In this paper, we investigate a relationship between energy and size of a threshold circuit processing a simple task, called PLRn, that was introduced in a context of pattern recognition. Formally, P LRn: {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 PLRn 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 PLRn 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 PLRn cannot be computed by any threshold circuit of energy e = 1 and size s ≤ ⌊n/2⌋ - 1.

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U2 - 10.1007/978-3-642-38236-9_23

DO - 10.1007/978-3-642-38236-9_23

M3 - Conference contribution

AN - SCOPUS:84893506841

SN - 9783642382352

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

SP - 248

EP - 259

BT - Theory and Applications of Models of Computation - 10th International Conference, TAMC 2013, Proceedings

PB - Springer Verlag

T2 - 10th International Conference on Theory and Applications of Models of Computation, TAMC 2013

Y2 - 20 May 2013 through 22 May 2013

ER -