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In this paper a new modeling framework for the dependability analysis of complex systems is presented and related to dynamic fault trees (DFTs). The methodology is based on a modular approach: two separate models are used to handle, the fault logic and the stochastic dependencies of the system. Thus, the fault schema, free of any dependency logic, can be easily evaluated, while the dependency schema allows the modeler to design new kind of non-trivial dependencies not easily caught by the traditional holistic methodologies. Moreover, the use of a dependency schema allows building a pure behavioral model that can be used for various kinds of dependability studies. In the paper is shown how to build and integrate the two modular models and convert them in a Stochastic Activity Network. Furthermore, based on the construction of the schema that embeds the stochastic dependencies, the procedure to convert DFTs into static fault trees is shown, allowing the resolution of DFTs in a very efficient way.
This paper will illustrate two versions of an algorithm for finding prime number up to N, which give the first version complexity
where c1, c2 are constants, and N is the input dimension, and gives a better result for the second version. The method is based on an equation that expresses the behavior of not prime numbers. With this equation it is possible to construct a fast iteration to verify if the not prime number is generated by a prime and with which parameters. The second method differs because it does not pass other times over a number that has been previously evaluated as not prime. This is possible for a recurrence of not prime number that is (mod 3) = 0. The complexity in this case is better than the first. The comparison is made most with Mathematics than by computer calculation as the number N should be very big to appreciate the difference between the two versions. Anyway the second version results better. The algorithms have been
In this paper we will give an algorithm that in the worst case solve the question about the primality of a number in but that gives better result if the number is not prime (constant operation). Firstly, we will introduce an equation on which are based not prime numbers. With this equation it is possible to deduce the prime number that generates a not prime number and to establish an equation in which if exists a certain integer the number is not prime and therefore vice versa to deduce if it is prime.