Even circuits

.ANALOG CIRCUITS Edited by Yuping Wu .Analog Circuits http://dx.doi.org/10.5772/45891 Edited by Yuping Wu Contributors Tales Pimenta, Gustavo Della Colletta, Odilon Dutra, Paulo Cesar Crepaldi, Leonardo Zoccal, Luis Ferreira, Tomasz Golonek, Piotr Jantos, Fawzi Mohammed Munir Al-Naima, Bessam Al-Jewad, Soumyasanta Laha, Savas Kaya, Zygmunt Garczarczyk Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2013 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.

128p namde01 11-04-2013 58 2   Download

In order to synthesize automat (in this case digital counters), the minimizing internal states is of particular significance and plays a decisive role in the results of synthetic circuit. This can be done in many ways, but the use of Karnaugh map is considered optimal. However, this process has some disadvantages that it can not be overcome when the number of input variants is large. In experience, if the number of variants is 7, manual minimization of circuit functions using Karnaugh map arises many difficulties and even become impossible if over 10 variants are available.

10p tuanlocmuido 19-12-2012 39 4   Download

A simple q-analogue of the sum of cubes is given. This answers a question posed in this journal by Garrett and Hummel.In their paper Garrett and Hummel commiserate the fact that (1) is not as simple as one might have hoped, and ask for a simpler sum of q-cubes. In response to this I propose the identity

2p thulanh5 12-09-2011 53 3   Download

We propose two alternative measures of the local irregularity of a graph in terms of its vertex degrees and relate these measures to the order and the global irregularity of the graph measured by the difference of its maximum and minimum vertex degree.All graphs will be simple and finite. Let G = (V,E) be a graph of order n = |V |. The degree and the neighbourhood of a vertex u 2 V will be denoted by d(u) and N(u). The maximum and minimum degree of G will be denoted by
(G) and (G).

6p thulanh5 12-09-2011 56 3   Download

A combinatorial bijection between k-edge colored trees and colored Pr¨ufer codes for labelled trees is established. This bijection gives a simple combinatorial proof for the number k(n − 2)!nk−n n−2
of k-edge colored trees with n vertices.A k-edge colored tree is a labelled tree whose edges are colored from a set of k colors such that any two edges with a common vertex have different colors

7p thulanh5 12-09-2011 84 7   Download

It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at least 2pd − 1 cos(  2k ). A similar result has been proved by Friedman using more sophisticated tools.More generally, Serre has shown (see [3], [4] ) that for any fixed r and for any infinite family of d-regular graphs Gi, lim inf r(Gi) 2pd − 1. The same result has been proved by Friedman already in [5].

4p thulanh5 12-09-2011 96 6   Download

When can a d-dimensional rectangular box R be tiled by translates of two given d-dimensional rectangular bricks B1 and B2? We prove that R can be tiled by translates of B1 and B2 if and only if R can be partitioned by a hyperplane into two sub-boxes R1 and R2 such that Ri can be tiled by translates of the brick Bi alone (i = 1, 2). Thus an obvious sufficient condition for a tiling is also a necessary condition. (However, there may be tilings that do not give rise to a bipartition of R.)

9p thulanh5 12-09-2011 62 6   Download

We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type A). One criterion utilizes totally nonnegative polynomials and the other utilizes Schur functions.The Bruhat order on Sn is often defined by comparing permutations = (1) · · ·(n) and = (1) · · ·(n) according to the following criterion..

4p thulanh5 12-09-2011 61 3   Download

Let G be a graph with vertex set V (G) = {1, . . . , n} and edge set E(G). We are interested in studying the functions of the graph G whose values belong to the interval [(G), (G)]. Here (G) is the size of the largest stable set in G and (G) is the smallest number of cliques that cover the vertices of G. It is well known (see, for example, [1]) that for some  0 it is impossible to approximate in polynomial time (G) and (G) within a factor of n, assuming P 6= NP. We suppose that better approximation could...

5p thulanh5 12-09-2011 65 4   Download

We gave a new criterion for graphical partitions. We derive a new recursion formula, which allows the computation of the number g(n) of graphical partitions of weight n for up to n 900.A partition of weight n is a nonincreasing sequence of nonnegative integers (1, 2, . . . , k, . . .) whose sum is n. The weight is denoted by ||. The number of nonzero elements in the sequence is the length of the partition denoted by l(). The set of all partitions of weight n is denoted by P(n).

17p thulanh5 12-09-2011 53 4   Download

The class of square (0, 1,−1)-matrices whose rows are nonzero and mutually orthogonal is studied. This class generalizes the classes of Hadamard and Weighing matrices. We prove that if there exists an n by n (0, 1,−1)-matrix whose rows are nonzero, mutually orthogonal and whose first row has no zeros, then n is not of the form pk, 2pk or 3p where p is an odd prime, and k is a positive integer.

9p thulanh5 12-09-2011 47 3   Download

A defensive alliance in a graph G = (V,E) is a set of vertices S  V satisfying the condition that for every vertex v 2 S, the number of neighbors v has in S plus one (counting v) is at least as large as the number of neighbors it has in V − S. Because of such an alliance, the vertices in S, agreeing to mutually support each other, have the strength of numbers to be able to defend themselves from the vertices in V − S. A defensive alliance S is called global if it effects every vertex in V − S, that is,...

13p thulanh5 12-09-2011 40 3   Download

Consider the problem of finding a large induced acyclic subgraph of a given simple digraph D = (V,E). The decision version of this problem is NP-complete and its optimization is not likely to be approximable within a ratio of O(n) for some  0. We study this problem when D is a random instance. We show that, almost surely, any maximal solution is within an o(ln n) factor from the optimal one. In addition, except when D is very sparse (having n1+o(1) edges), this ratio is in fact O(1). Thus, the optimal solution can be approximated in a much better way over random instances....

6p thulanh5 12-09-2011 43 4   Download

We show that a graph has an orientation under which every circuit of even length is clockwise odd if and only if the graph contains no subgraph which is, after the contraction of at most one circuit of odd length, an even subdivision of K2,3. In fact we give a more general characterisation of graphs that have an orientation under which every even circuit has a prescribed clockwise parity. Moreover we show that this characterisation has an equivalent analogue for signed graphs.

20p thulanh5 12-09-2011 49 2   Download

The basic distinction between already known algorithmic characterizations of matroids and antimatroids is in the fact that for antimatroids the ordering of elements is of great importance. While antimatroids can also be characterized as set systems, the question whether there is an algorithmic description of antimatroids in terms of sets and set functions was open for some period of time.

9p thulanh5 12-09-2011 50 4   Download

We establish three identities involving Dyck paths and alternating Motzkin paths, whose proofs are based on variants of the same bijection. We interpret these identities in terms of closed random walks on the halfline. We explain how these identities arise from combinatorial interpretations of certain properties of the -Hermite and -Laguerre ensembles of random matrix theory. We conclude by presenting two other identities obtained in the same way, for which finding combinatorial proofs is an open problem....

16p thulanh5 12-09-2011 70 4   Download

Tham khảo luận văn - đề án 'báo cáo khoa học: on a two-sided tur´an problem', luận văn - báo cáo, báo cáo khoa học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

17p thulanh5 12-09-2011 53 5   Download

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Bar´at and Hajnal on this subject and develop a generalization we call restricted arcwidth.

18p thulanh5 12-09-2011 56 4   Download

Hardware Acceleration of EDA Algorithms- P11: Single-threaded software applications have ceased to see significant gains in performance on a general-purpose CPU, even with further scaling in very large scale integration (VLSI) technology. This is a significant problem for electronic design automation (EDA) applications, since the design complexity of VLSI integrated circuits (ICs) is continuously growing.

7p xmen246 28-09-2010 90 4   Download

Hardware Acceleration of EDA Algorithms- P10: Single-threaded software applications have ceased to see significant gains in performance on a general-purpose CPU, even with further scaling in very large scale integration (VLSI) technology. This is a significant problem for electronic design automation (EDA) applications, since the design complexity of VLSI integrated circuits (ICs) is continuously growing.

20p xmen246 28-09-2010 74 5   Download