56 research outputs found
Exhaustive testing of combinatorial circuits
We present a method for the construction of s-surjective arrays, which allows exhaustive testing of any set of s
inputs in a combinatorial device . The method is based upon the use of linear codes, which implies simplicity of
implementation. The size (number of tests) of the obtained arrays is close to the minimum f (n, s) for values of th e
parameters n (total number of inputs) and s useful in practice .Nous présentons une méthode de construction de tableaux dits s-surjectifs qui permettent de tester exhaustivement
tout ensemble de s entrées d'un circuit combinatoire . La méthode est basée sur l'emploi de codes linéaires, c e
qui assure la simplicité de sa mise en œuvre. La taille (nombre de tests) des tableaux obtenus se rapproche d u
minimum f(n, s) pour certaines valeurs des paramètres n (nombre total d'entrées du circuit) et s utiles en
pratique
Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence
Consider the generalized iterated wreath product of symmetric groups. We give a complete description of the traversal
for the generalized iterated wreath product. We also prove an existence of a
bijection between the equivalence classes of ordinary irreducible
representations of the generalized iterated wreath product and orbits of labels
on certain rooted trees. We find a recursion for the number of these labels and
the degrees of irreducible representations of the generalized iterated wreath
product. Finally, we give rough upper bound estimates for fast Fourier
transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv
admin note: text overlap with arXiv:1409.060
An improved lower bound for (1,<=2)-identifying codes in the king grid
We call a subset of vertices of a graph a -identifying
code if for all subsets of vertices with size at most , the sets
are distinct. The concept of
identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin.
Identifying codes have been studied in various grids. In particular, it has
been shown that there exists a -identifying code in the king grid
with density 3/7 and that there are no such identifying codes with density
smaller than 5/12. Using a suitable frame and a discharging procedure, we
improve the lower bound by showing that any -identifying code of
the king grid has density at least 47/111
An Efficient Rank Based Approach for Closest String and Closest Substring
This paper aims to present a new genetic approach that uses rank distance for solving two known NP-hard problems, and to compare rank distance with other distance measures for strings. The two NP-hard problems we are trying to solve are closest string and closest substring. For each problem we build a genetic algorithm and we describe the genetic operations involved. Both genetic algorithms use a fitness function based on rank distance. We compare our algorithms with other genetic algorithms that use different distance measures, such as Hamming distance or Levenshtein distance, on real DNA sequences. Our experiments show that the genetic algorithms based on rank distance have the best results
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