Energy-Efficient Threshold Circuits for Comparison Functions
نویسندگان
چکیده
منابع مشابه
Energy-Efficient Threshold Circuits Computing Mod Functions
We prove that the modulus function MODm of n variables can be computed by a threshold circuit C of energy e and size s = O(e(n/m)1/(e−1)) for any integer e ≥ 2, where the energy e is defined to be the maximum number of gates outputting “1” over all inputs to C, and the size s to be the number of gates in C. Our upper bound on the size s almost matches the known lower bound s = Ω(e(n/m)1/e). We ...
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Let C be a threshold logic circuit computing a Boolean function MODm : {0, 1}n → {0, 1}, where n ≥ 1 and m ≥ 2. Then C outputs “0” if the number of “1”s in an input x ∈ {0, 1}n to C is a multiple of m and, otherwise, C outputs “1.” The function MOD2 is the so-called PARITY function, and MODn+1 is the OR function. Let s be the size of the circuit C, that is, C consists of s threshold gates, and ...
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We study the complexity of computing Boolean functions on general Boolean domains by polynomial threshold functions (PTFs). A typical example of a general Boolean domain is {1, 2}. We are mainly interested in the length (the number of monomials) of PTFs, with their degree and weight being of secondary interest. We show that PTFs on general Boolean domains are tightly connected to depth two thre...
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Weighted threshold functions with positive weights are a natural generalization of unweighted threshold functions. These functions are clearly monotone. However, the naive way of computing them is adding the weights of the satisfied variables and checking if the sum is greater than the threshold; this algorithm is inherently non-monotone since addition is a non-monotone function. In this work w...
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In his survey paper on branching programs, Razborov [RazSl] asked the following question: Does every rectifier-switching network computing the majority of n bits have size n l+n( l )? We answer this question in the negative by constructing a simple oblivious branching program of size n log3 n log log n log log log n for computing any threshold function. This improves the previously best known u...
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ژورنال
عنوان ژورنال: Interdisciplinary Information Sciences
سال: 2012
ISSN: 1340-9050,1347-6157
DOI: 10.4036/iis.2012.161