In this paper, we propose a genetic algorithm, called GenSPN, for finding highly probable differential characteristics of substitution permutation networks (SPNs). A special fitness function and a heuristic mutation operator have been used to improve the overall performance of the algorithm. We report our results of applying GenSPN for finding highly probable differential characteristics of Ser...

Crossover for evolutionary algorithms applied to permutation problems is a difficult and widely discussed topic. In this paper we use ideas from ant colony optimization to design a new permutation crossover operator. One of the advantages of the new crossover operator is the ease to introduce problem specific heuristic knowledge. Empirical tests on a travelling salesperson problem show that the...

Recently the operator algebra, including the twisted affine primary fields, and a set of twisted KZ equations were given for the WZW permutation orbifolds. In the first part of this paper we extend this operator algebra to include the so-called orbifold Virasoro algebra of each WZW permutation orbifold. These algebras generalize the orbifold Virasoro algebras (twisted Virasoro operators) found ...

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V⊗k . We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V⊗k are isomorphic to the categories of weak, weak admissible and ordinary V -modules, respectively. The main result is an explicit...