Genetic algorithm in the problem of obtaining minimal Boolean functions representations in the class of Kronecker forms

In this paper the algorithm of receiving the minimal complexity of Boolean function representations in the class of Kronecker forms based on evolutionary algorithm is constructed. Operator approach is used for function representation. Each Boolean function corresponds to unique representation, the special operator form. The obtained algorithm of receiving the minimal representation is based on the complexity of special operator form embedding in the classes of operator bundles, generated from single operator. The genetic algorithm is used to organize search by operators. The population consists of classes of operator bundles and the fitness function is defined as a complexity of special operator form embedding in the current class. The selection of candidates for next iteration is based on result of logarithmic function. Computational experiments have shown that results of genetic search for 9-variable Boolean functions correspond to the results of exact exhaustive search algorithm.