Regular realization of symmetric functions using reversible logic

2002 ◽  
Author(s):  
M. Perkowski ◽  
P. Kerntopf ◽  
A. Buller ◽  
M. Chrzanowska-Jeske ◽  
A. Mishchenko ◽  
...  
Keyword(s):  
Symmetric Functions ◽  
Reversible Logic

CHARACTERIZATION, TEST AND LOGIC SYNTHESIS OF NOVEL CONSERVATIVE AND REVERSIBLE LOGIC GATES FOR QCA

2010 ◽  
Vol 09 (03) ◽  
pp. 201-214 ◽  
Author(s):  
KUNAL DAS ◽  
DEBASHIS DE
Keyword(s):  
Low Power ◽  
Large Scale ◽  
Symmetric Functions ◽  
Logic Gate ◽  
Logic Synthesis ◽  
Vlsi Design ◽  
Logic Gates ◽  
Reversible Logic ◽  
Computing Paradigm ◽  
Scale Integration

Quantum dot cellular automaton (QCA) is an emerging technology in the field of nanotechnology. Reversible logic is emerging as a promising computing paradigm with applications in low-power quantum computing and QCA in the field of very large scale integration (VLSI) design. In this paper, we worked on conservative logic gate (CLG) and reversible logic gate (RLG). We examined that RLG and CLG are two classes of logic family intersecting each other. The intersection of RLG and CLG is parity preserving reversible (PPR) or conservative reversible logic gate (CRLG). We proposed in this paper, three algorithms to find different k × k RLG as well as CLG. Here, we demonstrate only the most promising two proposed gates of different categories. We compared the results with that of the previous Fredkin gate. The result shows that logic synthesis using above two gates will be a promising step towards the low-power QCA design era. We have shown a parity preserving approach to design all possible CLG. We also discuss a coupled Majority–minority-Voter (MmV) in a single nanostructure, dual outputs are driven simultaneously. This MmV gate is used for implementing n variables symmetric functions, testing the conservative gates as we explained that parity must be preserved if Majority and Minority output are same as input as well as output of CLG.

Algorithm of Optimizing Quantum Reversible Logic Synthesis

2009 ◽  
Vol 20 (9) ◽  
pp. 2332-2343
Author(s):  
Zhi-Qiang LI ◽  
Wen-Qian LI ◽  
Han-Wu CHEN
Keyword(s):  
Logic Synthesis ◽  
Reversible Logic ◽  
Reversible Logic Synthesis

CLASSES OF WEIGHTED SYMMETRIC FUNCTIONS

1988 ◽  
Vol 14 (2) ◽  
pp. 429
Author(s):  
Tran
Keyword(s):  
Symmetric Functions

WEIGHTED SYMMETRIC FUNCTIONS

1989 ◽  
Vol 15 (1) ◽  
pp. 313
Author(s):  
Tran
Keyword(s):  
Symmetric Functions

scholarly journals Applying Ateb–Gabor Filters to Biometric Imaging Problems

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 717
Author(s):  
Mariia Nazarkevych ◽  
Natalia Kryvinska ◽  
Yaroslav Voznyi
Keyword(s):  
Wavelet Transformation ◽  
Symmetric Functions ◽  
Gabor Filter ◽  
Signal To Noise Ratio ◽  
The Other ◽  
Mean Square ◽  
Image Transformation ◽  
Gabor Filtering ◽  
Signal To Noise ◽  
Filtration Method

This article presents a new method of image filtering based on a new kind of image processing transformation, particularly the wavelet-Ateb–Gabor transformation, that is a wider basis for Gabor functions. Ateb functions are symmetric functions. The developed type of filtering makes it possible to perform image transformation and to obtain better biometric image recognition results than traditional filters allow. These results are possible due to the construction of various forms and sizes of the curves of the developed functions. Further, the wavelet transformation of Gabor filtering is investigated, and the time spent by the system on the operation is substantiated. The filtration is based on the images taken from NIST Special Database 302, that is publicly available. The reliability of the proposed method of wavelet-Ateb–Gabor filtering is proved by calculating and comparing the values of peak signal-to-noise ratio (PSNR) and mean square error (MSE) between two biometric images, one of which is filtered by the developed filtration method, and the other by the Gabor filter. The time characteristics of this filtering process are studied as well.

scholarly journals A symmetric Bloch–Okounkov theorem

2021 ◽  
Vol 8 (2) ◽  
Author(s):  
Jan-Willem M. van Ittersum
Keyword(s):  
Symmetric Functions ◽  
Graded Algebra ◽  
Symmetric Polynomials ◽  
Generating Series

AbstractThe algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the q-bracket, is a quasimodular form. More generally, if a graded algebra A of functions on partitions has the property that the q-bracket of every element is a quasimodular form of the same weight, we call A a quasimodular algebra. We introduce a new quasimodular algebra $$\mathcal {T}$$ T consisting of symmetric polynomials in the part sizes and multiplicities.

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