2,186 research outputs found
Mathematical Estimation of Logical Masking Capability of Majority/Minority Gates Used in Nanoelectronic Circuits
In nanoelectronic circuit synthesis, the majority gate and the inverter form
the basic combinational logic primitives. This paper deduces the mathematical
formulae to estimate the logical masking capability of majority gates, which
are used extensively in nanoelectronic digital circuit synthesis. The
mathematical formulae derived to evaluate the logical masking capability of
majority gates holds well for minority gates, and a comparison with the logical
masking capability of conventional gates such as NOT, AND/NAND, OR/NOR, and
XOR/XNOR is provided. It is inferred from this research work that the logical
masking capability of majority/minority gates is similar to that of XOR/XNOR
gates, and with an increase of fan-in the logical masking capability of
majority/minority gates also increases
The Synthesis and Analysis of Stochastic Switching Circuits
Stochastic switching circuits are relay circuits that consist of stochastic
switches called pswitches. The study of stochastic switching circuits has
widespread applications in many fields of computer science, neuroscience, and
biochemistry. In this paper, we discuss several properties of stochastic
switching circuits, including robustness, expressibility, and probability
approximation.
First, we study the robustness, namely, the effect caused by introducing an
error of size \epsilon to each pswitch in a stochastic circuit. We analyze two
constructions and prove that simple series-parallel circuits are robust to
small error perturbations, while general series-parallel circuits are not.
Specifically, the total error introduced by perturbations of size less than
\epsilon is bounded by a constant multiple of \epsilon in a simple
series-parallel circuit, independent of the size of the circuit.
Next, we study the expressibility of stochastic switching circuits: Given an
integer q and a pswitch set S=\{\frac{1}{q},\frac{2}{q},...,\frac{q-1}{q}\},
can we synthesize any rational probability with denominator q^n (for arbitrary
n) with a simple series-parallel stochastic switching circuit? We generalize
previous results and prove that when q is a multiple of 2 or 3, the answer is
yes. We also show that when q is a prime number larger than 3, the answer is
no.
Probability approximation is studied for a general case of an arbitrary
pswitch set S=\{s_1,s_2,...,s_{|S|}\}. In this case, we propose an algorithm
based on local optimization to approximate any desired probability. The
analysis reveals that the approximation error of a switching circuit decreases
exponentially with an increasing circuit size.Comment: 2 columns, 15 page
BioSystems 97 (2009) 146β153 Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/biosystems A novel generalized design methodology and realization of Boolean operations using DN
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