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Fault diagnosis of interconnection networks is vital to ensuring the reliability and maintenance of multiprocessor systems. Based on graph theory, diagnostic algorithms for solving the problem of fault diagnosis in interconnection networks have been widely studied. As the number of processors in multiprocessor systems has increased in recent years, fault diagnosis algorithms based on graph theory cannot meet the current diagnosis requirements of some interconnection networks, such as t-diagnosable systems. In this paper, we use the evolution diagnosis approach to study fault diagnosis in t-diagnosable systems under the PMC model. First, for a t-diagnosable system G with a syndrome σ , we use a simple centralized algorithm to generate its simplified diagnosis graph G f , which contains all the faulty nodes in G. Based on the graph, we prove that the faulty node set in G is the minimum cover set of G f . Next, we prove that the problem of computing the minimum cover set for G f is equivalent to the problem of computing the optimal solution of a zero-one integer program. Using this result, we propose a novel genetic algorithm to solve the problem of the zero-one integer program. The simulation results show that the diagnostic accuracy of our proposed algorithm is equal to or greater than 96% and that the proposed algorithm outperforms its competitors in terms of diagnostic accuracy, number of iterations and running time. [ABSTRACT FROM AUTHOR]

The paper considers the disadvantages of existing approaches to testing software and hardware data security tools in order to confirm compliance of the implemented functionality with the declared characteristics. It demonstrates the necessity of ensuring completeness and optimality of testing. The paper describes some testing approaches based on the development of mathematical models using the automata theory and ensuring completeness of testing, but leaving the question of its optimality open. It describes the approach proposed earlier by the authors, which ensures both completeness and optimality of testing using the graph theory. In accordance with this approach, the software and hardware data security tool is represented as a directed graph without loops or multiple edges. The graph vertices correspond to the states of the software or hardware component, and the directed edges correspond to the transitions of the data security tool from one state to another when performing non-target functions or security functions. On the basis of this approach, the authors propose an algorithm for solving the problem of testing software and hardware data security tools using a number of well-known algorithms on graphs. In the paper, it is substantiated that a solution to the problem of ensuring completeness and optimality of testing exists if and only if any vertex of the derived graph obtained by removing all unused vertices and edges either belongs to a directed chain or lies in a strongly connected component. Application of the proposed algorithm for solving the problem of testing one of the software and hardware security tools is considered, and the possibility of its application in practice is confirmed. [ABSTRACT FROM AUTHOR]