Classification of Ternary Logic Functions by Self-Dual Equivalence Classes

2011 ◽  
Author(s):  
Takako Soma ◽  
Takashi Soma
Keyword(s):  
Equivalence Classes ◽  
Ternary Logic ◽  
Dual Equivalence ◽  
Logic Functions

scholarly journals Implementation of Unbalanced Ternary Logic Gates with the Combination of Spintronic Memristor and CMOS

Electronics ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 542 ◽  
Author(s):  
Haifeng Zhang ◽  
Zhaowei Zhang ◽  
Mingyu Gao ◽  
Li Luo ◽  
Shukai Duan ◽  
...  
Keyword(s):  
High Efficiency ◽  
Load Capacity ◽  
Complementary Metal Oxide Semiconductor ◽  
Logic Gates ◽  
Logic Circuit ◽  
Oxide Semiconductor ◽  
Ternary Logic ◽  
Logic Operations ◽  
Almost All ◽  
Logic Functions

A memristor is a nanoscale electronic element that displays a threshold property, non-volatility, and variable conductivity. Its composite circuits are promising for the implementation of intelligence computation, especially for logic operations. In this paper, a flexible logic circuit composed of a spintronic memristor and complementary metal-oxide-semiconductor (CMOS) switches is proposed for the implementation of the basic unbalanced ternary logic gates, including the NAND, NOR, AND, and OR gates. Meanwhile, due to the participation of the memristor and CMOS, the proposed circuit has advantages in terms of non-volatility and load capacity. Furthermore, the input and output of the proposed logic are both constant voltages without signal degradation. All these three merits make the proposed circuit capable of realizing the cascaded logic functions. In order to demonstrate the validity and effectiveness of the entire work, series circuit simulations were carried out. The experimental results indicated that the proposed logic circuit has the potential to realize almost all basic ternary logic gates, and even some more complicated cascaded logic functions with a compact circuit construction, high efficiency, and good robustness.

scholarly journals Classification of fused links

2016 ◽  
Vol 25 (14) ◽  
pp. 1650076 ◽  
Author(s):  
Timur Nasybullov
Keyword(s):  
Symmetric Group ◽  
Equivalence Classes ◽  
One To One ◽  
Text Component

We construct the complete invariant for fused links. It is proved that the set of equivalence classes of [Formula: see text]-component fused links is in one-to-one correspondence with the set of elements of the abelization [Formula: see text] up to conjugation by elements from the symmetric group [Formula: see text].

Computing the Number of the Equivalence Classes for Reversible Logic Functions

2020 ◽  
Vol 59 (8) ◽  
pp. 2384-2396
Author(s):  
Qing-bin Luo ◽  
Guo-wu Yang ◽  
Jin-zhao Wu ◽  
Chen Lin
Keyword(s):  
Reversible Logic ◽  
Equivalence Classes ◽  
Logic Functions

scholarly journals A classification of intersection type systems

2002 ◽  
Vol 67 (1) ◽  
pp. 353-368
Author(s):  
M. W. Bunder
Keyword(s):  
Type Systems ◽  
Equivalence Classes ◽  
Type Assignment ◽  
Emptiness Problem ◽  
Intersection Types

AbstractThe first system of intersection types. Coppo and Dezani [3], extended simple types to include intersections and added intersection introduction and elimination rules ((ΛI ) and (ΛE) ) to the type assignment system. The major advantage of these new types was that they were invariant under β-equality, later work by Barendregt, Coppo and Dezani [1], extended this to include an (η) rule which gave types invariant under βη-reduction.Urzyczyn proved in [6] that for both these systems it is undecidable whether a given intersection type is empty. Kurata and Takahashi however have shown in [5] that this emptiness problem is decidable for the sytem including (η). but without (ΛI).The aim of this paper is to classify intersection type systems lacking some of (ΛI), (ΛE) and (η), into equivalence classes according to their strength in typing λ-terms and also according to their strength in possessing inhabitants.This classification is used in a later paper to extend the above (un)decidability results to two of the five inhabitation-equivalence classes. This later paper also shows that the systems in two more of these classes have decidable inhabitation problems and develops algorithms to find such inhabitants.

A new classification of logic functions of three variables

1981 ◽  
Vol 69 (12) ◽  
pp. 1592-1594
Author(s):  
S. Ragupathi ◽  
G. Venkateswardu ◽  
M.P. Singh
Keyword(s):  
New Classification ◽  
Logic Functions

scholarly journals Asymptotics for the Number of Simple (4a + 1)-knots of Genus 1

2020 ◽  
Author(s):  
Alison Beth Miller
Keyword(s):  
Quadratic Forms ◽  
Alexander Polynomial ◽  
Equivalence Classes ◽  
Binary Quadratic Forms ◽  
Sieve Methods

Abstract We investigate the asymptotics of the total number of simple $(4a+1)$-knots with Alexander polynomial of the form $mt^2 +(1-2m) t + m$ for some nonzero $m \in [-X, X]$. Using Kearton and Levine’s classification of simple knots, we give equivalent algebraic and arithmetic formulations of this counting question. In particular, this count is the same as the total number of ${\mathbb{Z}}[1/m]$-equivalence classes of binary quadratic forms of discriminant $1-4m$, for $m$ running through the same range. Our heuristics, based on the Cohen–Lenstra heuristics, suggest that this total is asymptotic to $X^{3/2}/\log X$ and the largest contribution comes from the values of $m$ that are positive primes. Using sieve methods, we prove that the contribution to the total coming from $m$ positive prime is bounded above by $O(X^{3/2}/\log X)$ and that the total itself is $o(X^{3/2})$.

scholarly journals Classification of pointed fusion categories of dimension p3 up to weak Morita Equivalence

2020 ◽  
pp. 2140008
Author(s):  
Kevin Maya ◽  
Adriana Mejía Castaño ◽  
Bernardo Uribe
Keyword(s):  
Complete Classification ◽  
Global Dimension ◽  
Morita Equivalence ◽  
Equivalence Classes ◽  
Fusion Categories ◽  
Dimension Formula ◽  
Equivalent Categories

We give a complete classification of pointed fusion categories over [Formula: see text] of global dimension [Formula: see text] for [Formula: see text] any odd prime. We proceed to classify the equivalence classes of pointed fusion categories of dimension [Formula: see text] and we determine which of these equivalence classes have equivalent categories of modules.

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